LMFDB - Embedded newform 315.2.bo.b.4.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(4,315)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("315.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bo (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.6
Character	$\chi$	$=$	315.4
Dual form			315.2.bo.b.79.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.90125 - 1.09768i) q^{2} +(-1.70434 - 0.308593i) q^{3} +(1.40982 + 2.44189i) q^{4} +(-1.91379 + 1.15647i) q^{5} +(2.90163 + 2.45754i) q^{6} +(-2.51786 - 0.812625i) q^{7} -1.79943i q^{8} +(2.80954 + 1.05190i) q^{9} +O(q^{10})$	\(q+(-1.90125 - 1.09768i) q^{2} +(-1.70434 - 0.308593i) q^{3} +(1.40982 + 2.44189i) q^{4} +(-1.91379 + 1.15647i) q^{5} +(2.90163 + 2.45754i) q^{6} +(-2.51786 - 0.812625i) q^{7} -1.79943i q^{8} +(2.80954 + 1.05190i) q^{9} +(4.90802 - 0.0979947i) q^{10} -4.88811 q^{11} +(-1.64927 - 4.59686i) q^{12} +(3.33423 + 1.92502i) q^{13} +(3.89507 + 4.30882i) q^{14} +(3.61862 - 1.38043i) q^{15} +(0.844442 - 1.46262i) q^{16} +(2.70647 + 1.56258i) q^{17} +(-4.18698 - 5.08390i) q^{18} +(0.0763587 + 0.132257i) q^{19} +(-5.52207 - 3.04284i) q^{20} +(4.04052 + 2.16199i) q^{21} +(9.29350 + 5.36561i) q^{22} -6.71452i q^{23} +(-0.555292 + 3.06684i) q^{24} +(2.32516 - 4.42647i) q^{25} +(-4.22613 - 7.31987i) q^{26} +(-4.46380 - 2.65979i) q^{27} +(-1.56541 - 7.29400i) q^{28} +(-0.154423 - 0.267468i) q^{29} +(-8.39516 - 1.34757i) q^{30} +(-0.0255899 - 0.0443229i) q^{31} +(-6.32768 + 3.65329i) q^{32} +(8.33100 + 1.50844i) q^{33} +(-3.43044 - 5.94170i) q^{34} +(5.75843 - 1.35664i) q^{35} +(1.39235 + 8.34356i) q^{36} +(-1.80731 + 1.04345i) q^{37} -0.335271i q^{38} +(-5.08861 - 4.30980i) q^{39} +(2.08098 + 3.44372i) q^{40} +(5.42923 - 9.40369i) q^{41} +(-5.30885 - 8.54568i) q^{42} +(2.65699 - 1.53401i) q^{43} +(-6.89138 - 11.9362i) q^{44} +(-6.59335 + 1.23604i) q^{45} +(-7.37042 + 12.7659i) q^{46} +(11.4749 + 6.62506i) q^{47} +(-1.89057 + 2.23220i) q^{48} +(5.67928 + 4.09216i) q^{49} +(-9.27957 + 5.86351i) q^{50} +(-4.13054 - 3.49836i) q^{51} +10.8557i q^{52} +(0.160285 + 0.0925406i) q^{53} +(5.56717 + 9.95676i) q^{54} +(9.35481 - 5.65294i) q^{55} +(-1.46226 + 4.53072i) q^{56} +(-0.0893274 - 0.248975i) q^{57} +0.678030i q^{58} +(5.87781 + 10.1807i) q^{59} +(8.47247 + 6.89009i) q^{60} +(1.73004 - 2.99652i) q^{61} +0.112358i q^{62} +(-6.21924 - 4.93163i) q^{63} +12.6629 q^{64} +(-8.60723 + 0.171854i) q^{65} +(-14.1835 - 12.0127i) q^{66} +(-2.85723 + 1.64962i) q^{67} +8.81185i q^{68} +(-2.07206 + 11.4438i) q^{69} +(-12.4374 - 3.74164i) q^{70} +5.16993 q^{71} +(1.89281 - 5.05557i) q^{72} +(0.870104 + 0.502355i) q^{73} +4.58151 q^{74} +(-5.32884 + 6.82667i) q^{75} +(-0.215305 + 0.372918i) q^{76} +(12.3076 + 3.97220i) q^{77} +(4.94389 + 13.7797i) q^{78} +(-5.44799 + 9.43619i) q^{79} +(0.0753867 + 3.77570i) q^{80} +(6.78703 + 5.91068i) q^{81} +(-20.6446 + 11.9192i) q^{82} +(1.85528 - 1.07115i) q^{83} +(0.417103 + 12.9145i) q^{84} +(-6.98668 + 0.139498i) q^{85} -6.73545 q^{86} +(0.180650 + 0.503510i) q^{87} +8.79581i q^{88} +(2.49724 + 4.32534i) q^{89} +(13.8924 + 4.88740i) q^{90} +(-6.83082 - 7.55642i) q^{91} +(16.3961 - 9.46629i) q^{92} +(0.0299360 + 0.0834381i) q^{93} +(-14.5444 - 25.1917i) q^{94} +(-0.299085 - 0.164806i) q^{95} +(11.9119 - 4.27376i) q^{96} +(-4.67963 + 2.70179i) q^{97} +(-6.30580 - 14.0143i) q^{98} +(-13.7333 - 5.14178i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9}+O(q^{10}) $ 84 * q + 44 * q^4 - 6 * q^5 + 6 * q^6 - 14 * q^9	$ 84 q + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9} + 6 q^{10} - 24 q^{11} - 10 q^{14} + 4 q^{15} - 36 q^{16} + 8 q^{19} - 10 q^{20} - 14 q^{21} + 18 q^{24} + 10 q^{25} - 40 q^{26} - 10 q^{29} - 28 q^{30} - 6 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} + 4 q^{39} - 8 q^{40} - 30 q^{41} - 4 q^{44} - 30 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} + 14 q^{51} + 18 q^{54} - 54 q^{55} + 48 q^{56} + 42 q^{59} + 66 q^{60} + 22 q^{61} - 28 q^{64} + 8 q^{65} - 38 q^{66} - 32 q^{69} - 26 q^{70} - 4 q^{71} - 108 q^{74} + 6 q^{75} + 24 q^{76} + 24 q^{79} - 9 q^{80} - 106 q^{81} - 64 q^{84} + q^{85} - 92 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} - 8 q^{94} - 25 q^{95} + 54 q^{96} - 102 q^{99}+O(q^{100}) $ 84 * q + 44 * q^4 - 6 * q^5 + 6 * q^6 - 14 * q^9 + 6 * q^10 - 24 * q^11 - 10 * q^14 + 4 * q^15 - 36 * q^16 + 8 * q^19 - 10 * q^20 - 14 * q^21 + 18 * q^24 + 10 * q^25 - 40 * q^26 - 10 * q^29 - 28 * q^30 - 6 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 + 4 * q^39 - 8 * q^40 - 30 * q^41 - 4 * q^44 - 30 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 + 14 * q^51 + 18 * q^54 - 54 * q^55 + 48 * q^56 + 42 * q^59 + 66 * q^60 + 22 * q^61 - 28 * q^64 + 8 * q^65 - 38 * q^66 - 32 * q^69 - 26 * q^70 - 4 * q^71 - 108 * q^74 + 6 * q^75 + 24 * q^76 + 24 * q^79 - 9 * q^80 - 106 * q^81 - 64 * q^84 + q^85 - 92 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 - 8 * q^94 - 25 * q^95 + 54 * q^96 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.90125	−	1.09768i	−1.34438	−	0.776180i	−0.356936	−	0.934129i	$-0.616179\pi$
$2$	−1.90125	−	1.09768i	−1.34438	−	0.776180i	−0.987447	+	0.157948i	$0.949512\pi$
$3$	−1.70434	−	0.308593i	−0.984000	−	0.178166i
$3$	−1.70434	−	0.308593i	−0.984000	−	0.178166i
$4$	1.40982	+	2.44189i	0.704912	+	1.22094i
$5$	−1.91379	+	1.15647i	−0.855872	+	0.517188i
$5$	−1.91379	+	1.15647i	−0.855872	+	0.517188i
$6$	2.90163	+	2.45754i	1.18458	+	1.00329i
$7$	−2.51786	−	0.812625i	−0.951663	−	0.307144i
$7$	−2.51786	−	0.812625i	−0.951663	−	0.307144i
$8$		−	1.79943i		−	0.636194i
$9$	2.80954	+	1.05190i	0.936513	+	0.350632i
$10$	4.90802	−	0.0979947i	1.55205	−	0.0309887i
$11$	−4.88811			−1.47382			−0.736911	−	0.675990i	$-0.763716\pi$
$11$	−4.88811			−1.47382			−0.736911	+	0.675990i	$0.763716\pi$
$12$	−1.64927	−	4.59686i	−0.476102	−	1.32700i
$13$	3.33423	+	1.92502i	0.924749	+	0.533904i	0.885147	−	0.465311i	$-0.154058\pi$
$13$	3.33423	+	1.92502i	0.924749	+	0.533904i	0.0396020	+	0.999216i	$0.487391\pi$
$14$	3.89507	+	4.30882i	1.04100	+	1.15158i
$15$	3.61862	−	1.38043i	0.934324	−	0.356426i
$16$	0.844442	−	1.46262i	0.211110	−	0.365654i
$17$	2.70647	+	1.56258i	0.656415	+	0.378981i	0.790910	−	0.611933i	$-0.209608\pi$
$17$	2.70647	+	1.56258i	0.656415	+	0.378981i	−0.134495	+	0.990914i	$0.542941\pi$
$18$	−4.18698	−	5.08390i	−0.986880	−	1.19829i
$19$	0.0763587	+	0.132257i	0.0175179	+	0.0303419i	0.874651	−	0.484752i	$-0.161090\pi$
$19$	0.0763587	+	0.132257i	0.0175179	+	0.0303419i	−0.857134	+	0.515094i	$0.827757\pi$
$20$	−5.52207	−	3.04284i	−1.23477	−	0.680399i
$21$	4.04052	+	2.16199i	0.881714	+	0.471784i
$22$	9.29350	+	5.36561i	1.98138	+	1.14395i
$23$		−	6.71452i		−	1.40007i	−0.714107	−	0.700037i	$-0.753167\pi$
$23$		−	6.71452i		−	1.40007i	0.714107	−	0.700037i	$-0.246833\pi$
$24$	−0.555292	+	3.06684i	−0.113348	+	0.626015i
$25$	2.32516	−	4.42647i	0.465033	−	0.885293i
$26$	−4.22613	−	7.31987i	−0.828812	−	1.43554i
$27$	−4.46380	−	2.65979i	−0.859059	−	0.511877i
$28$	−1.56541	−	7.29400i	−0.295834	−	1.37844i
$29$	−0.154423	−	0.267468i	−0.0286756	−	0.0496675i	0.851331	−	0.524628i	$-0.175796\pi$
$29$	−0.154423	−	0.267468i	−0.0286756	−	0.0496675i	−0.880007	+	0.474961i	$0.842462\pi$
$30$	−8.39516	−	1.34757i	−1.53274	−	0.246031i
$31$	−0.0255899	−	0.0443229i	−0.00459607	−	0.00796063i	0.863718	−	0.503975i	$-0.168130\pi$
$31$	−0.0255899	−	0.0443229i	−0.00459607	−	0.00796063i	−0.868314	+	0.496014i	$0.834796\pi$
$32$	−6.32768	+	3.65329i	−1.11859	+	0.645817i
$33$	8.33100	+	1.50844i	1.45024	+	0.262585i
$34$	−3.43044	−	5.94170i	−0.588316	−	1.01899i
$35$	5.75843	−	1.35664i	0.973353	−	0.229314i
$36$	1.39235	+	8.34356i	0.232058	+	1.39059i
$37$	−1.80731	+	1.04345i	−0.297119	+	0.171542i	−0.641148	−	0.767417i	$-0.721542\pi$
$37$	−1.80731	+	1.04345i	−0.297119	+	0.171542i	0.344029	+	0.938959i	$0.388208\pi$
$38$		−	0.335271i		−	0.0543881i
$39$	−5.08861	−	4.30980i	−0.814830	−	0.690121i
$40$	2.08098	+	3.44372i	0.329032	+	0.544501i
$41$	5.42923	−	9.40369i	0.847903	−	1.46861i	−0.0351739	−	0.999381i	$-0.511199\pi$
$41$	5.42923	−	9.40369i	0.847903	−	1.46861i	0.883076	−	0.469229i	$-0.155468\pi$
$42$	−5.30885	−	8.54568i	−0.819173	−	1.31863i
$43$	2.65699	−	1.53401i	0.405187	−	0.233935i	−0.283533	−	0.958963i	$-0.591506\pi$
$43$	2.65699	−	1.53401i	0.405187	−	0.233935i	0.688720	+	0.725028i	$0.258173\pi$
$44$	−6.89138	−	11.9362i	−1.03891	−	1.79945i
$45$	−6.59335	+	1.23604i	−0.982878	+	0.184258i
$46$	−7.37042	+	12.7659i	−1.08671	+	1.88224i
$47$	11.4749	+	6.62506i	1.67379	+	0.966364i	0.965485	+	0.260459i	$0.0838739\pi$
$47$	11.4749	+	6.62506i	1.67379	+	0.966364i	0.708307	+	0.705905i	$0.249459\pi$
$48$	−1.89057	+	2.23220i	−0.272880	+	0.322191i
$49$	5.67928	+	4.09216i	0.811326	+	0.584594i
$50$	−9.27957	+	5.86351i	−1.31233	+	0.829225i
$51$	−4.13054	−	3.49836i	−0.578391	−	0.489869i
$52$			10.8557i			1.50542i
$53$	0.160285	+	0.0925406i	0.0220168	+	0.0127114i	0.510968	−	0.859600i	$-0.329287\pi$
$53$	0.160285	+	0.0925406i	0.0220168	+	0.0127114i	−0.488951	+	0.872311i	$0.662620\pi$
$54$	5.56717	+	9.95676i	0.757596	+	1.35494i
$55$	9.35481	−	5.65294i	1.26140	−	0.762243i
$56$	−1.46226	+	4.53072i	−0.195403	+	0.605443i
$57$	−0.0893274	−	0.248975i	−0.0118317	−	0.0329775i
$58$			0.678030i			0.0890296i
$59$	5.87781	+	10.1807i	0.765226	+	1.32541i	0.940127	+	0.340824i	$0.110706\pi$
$59$	5.87781	+	10.1807i	0.765226	+	1.32541i	−0.174902	+	0.984586i	$0.555961\pi$
$60$	8.47247	+	6.89009i	1.09379	+	0.889507i
$61$	1.73004	−	2.99652i	0.221509	−	0.383665i	−0.733757	−	0.679412i	$-0.762235\pi$
$61$	1.73004	−	2.99652i	0.221509	−	0.383665i	0.955266	+	0.295747i	$0.0955684\pi$
$62$			0.112358i			0.0142695i
$63$	−6.21924	−	4.93163i	−0.783551	−	0.621327i
$64$	12.6629			1.58286
$65$	−8.60723	+	0.171854i	−1.06760	+	0.0213159i
$66$	−14.1835	−	12.0127i	−1.74587	−	1.47866i
$67$	−2.85723	+	1.64962i	−0.349066	+	0.201533i	−0.664274	−	0.747489i	$-0.731259\pi$
$67$	−2.85723	+	1.64962i	−0.349066	+	0.201533i	0.315208	+	0.949023i	$0.397926\pi$
$68$			8.81185i			1.06859i
$69$	−2.07206	+	11.4438i	−0.249446	+	1.37767i
$70$	−12.4374	−	3.74164i	−1.48655	−	0.447212i
$71$	5.16993			0.613558			0.306779	−	0.951781i	$-0.400749\pi$
$71$	5.16993			0.613558			0.306779	+	0.951781i	$0.400749\pi$
$72$	1.89281	−	5.05557i	0.223070	−	0.595804i
$73$	0.870104	+	0.502355i	0.101838	+	0.0587962i	0.550054	−	0.835129i	$-0.314607\pi$
$73$	0.870104	+	0.502355i	0.101838	+	0.0587962i	−0.448216	+	0.893925i	$0.647940\pi$
$74$	4.58151			0.532590
$75$	−5.32884	+	6.82667i	−0.615322	+	0.788276i
$76$	−0.215305	+	0.372918i	−0.0246971	+	0.0427767i
$77$	12.3076	+	3.97220i	1.40258	+	0.452675i
$78$	4.94389	+	13.7797i	0.559785	+	1.56024i
$79$	−5.44799	+	9.43619i	−0.612946	+	1.06165i	0.377795	+	0.925889i	$0.376683\pi$
$79$	−5.44799	+	9.43619i	−0.612946	+	1.06165i	−0.990741	+	0.135765i	$0.956651\pi$
$80$	0.0753867	+	3.77570i	0.00842849	+	0.422137i
$81$	6.78703	+	5.91068i	0.754115	+	0.656743i
$82$	−20.6446	+	11.9192i	−2.27981	+	1.31625i
$83$	1.85528	−	1.07115i	0.203644	−	0.117574i	−0.394710	−	0.918806i	$-0.629155\pi$
$83$	1.85528	−	1.07115i	0.203644	−	0.117574i	0.598354	+	0.801232i	$0.295822\pi$
$84$	0.417103	+	12.9145i	0.0455096	+	1.40909i
$85$	−6.98668	+	0.139498i	−0.757812	+	0.0151307i
$86$	−6.73545			−0.726303
$87$	0.180650	+	0.503510i	0.0193677	+	0.0539819i
$88$			8.79581i			0.937637i
$89$	2.49724	+	4.32534i	0.264707	+	0.458486i	0.967487	−	0.252922i	$-0.0813915\pi$
$89$	2.49724	+	4.32534i	0.264707	+	0.458486i	−0.702780	+	0.711407i	$0.748058\pi$
$90$	13.8924	+	4.88740i	1.46438	+	0.515177i
$91$	−6.83082	−	7.55642i	−0.716064	−	0.792128i
$92$	16.3961	−	9.46629i	1.70941	−	0.986929i
$93$	0.0299360	+	0.0834381i	0.00310422	+	0.00865213i
$94$	−14.5444	−	25.1917i	−1.50015	−	2.59833i
$95$	−0.299085	−	0.164806i	−0.0306855	−	0.0169087i
$96$	11.9119	−	4.27376i	1.21575	−	0.436189i
$97$	−4.67963	+	2.70179i	−0.475144	+	0.274325i	−0.718391	−	0.695640i	$-0.755121\pi$
$97$	−4.67963	+	2.70179i	−0.475144	+	0.274325i	0.243246	+	0.969965i	$0.421788\pi$
$98$	−6.30580	−	14.0143i	−0.636982	−	1.41565i
$99$	−13.7333	−	5.14178i	−1.38025	−	0.516768i
$100$	14.0870	−	0.562754i	1.40870	−	0.0562754i
$101$	1.33628			0.132965			0.0664823	−	0.997788i	$-0.478822\pi$
$101$	1.33628			0.132965			0.0664823	+	0.997788i	$0.478822\pi$
$102$	4.01307	+	11.1853i	0.397353	+	1.10751i
$103$		−	7.76061i		−	0.764676i	−0.924023	−	0.382338i	$-0.875119\pi$
$103$		−	7.76061i		−	0.764676i	0.924023	−	0.382338i	$-0.124881\pi$
$104$	3.46393	−	5.99971i	0.339667	−	0.588320i
$105$	−10.2330	+	0.535155i	−0.998635	+	0.0522258i
$106$	−0.203161	−	0.351885i	−0.0197327	−	0.0341781i
$107$	15.8775	−	9.16685i	1.53493	−	0.886193i	0.535808	−	0.844340i	$-0.320007\pi$
$107$	15.8775	−	9.16685i	1.53493	−	0.886193i	0.999124	−	0.0418531i	$-0.0133261\pi$
$108$	0.201735	−	14.6499i	0.0194119	−	1.40969i
$109$	5.93046	−	10.2719i	0.568035	−	0.983865i	−0.428725	−	0.903435i	$-0.641037\pi$
$109$	5.93046	−	10.2719i	0.568035	−	0.983865i	0.996760	−	0.0804303i	$-0.0256294\pi$
$110$	−23.9909	+	0.479009i	−2.28745	+	0.0456717i
$111$	3.40226	−	1.22067i	0.322929	−	0.115861i
$112$	−3.31475	+	2.99645i	−0.313214	+	0.283138i
$113$	−6.46189	−	3.73077i	−0.607883	−	0.350962i	0.164253	−	0.986418i	$-0.447479\pi$
$113$	−6.46189	−	3.73077i	−0.607883	−	0.350962i	−0.772137	+	0.635457i	$0.780812\pi$
$114$	−0.103462	+	0.571415i	−0.00969014	+	0.0535179i
$115$	7.76512	+	12.8502i	0.724102	+	1.19828i
$116$	0.435417	−	0.754165i	0.0404275	−	0.0700225i
$117$	7.34274	+	8.91568i	0.678836	+	0.824255i
$118$		−	25.8079i		−	2.37581i
$119$	−5.54473	−	6.13371i	−0.508284	−	0.562276i
$120$	−2.48399	−	6.51145i	−0.226756	−	0.594411i
$121$	12.8936			1.17215
$122$	−6.57846	+	3.79808i	−0.595586	+	0.343862i
$123$	−12.1552	+	14.3517i	−1.09599	+	1.29405i
$124$	0.0721544	−	0.124975i	0.00647965	−	0.0112231i
$125$	0.669199	+	11.1603i	0.0598550	+	0.998207i
$126$	6.41093	+	16.2030i	0.571131	+	1.44348i
$127$		−	0.617598i		−	0.0548029i	−0.999625	−	0.0274015i	$-0.991277\pi$
$127$		−	0.617598i		−	0.0548029i	0.999625	−	0.0274015i	$-0.00872325\pi$
$128$	−11.4199	−	6.59327i	−1.00938	−	0.582768i
$129$	−5.00180	+	1.79455i	−0.440384	+	0.158001i
$130$	16.5531	+	9.12129i	1.45180	+	0.799990i
$131$	3.56478			0.311456			0.155728	−	0.987800i	$-0.450228\pi$
$131$	3.56478			0.311456			0.155728	+	0.987800i	$0.450228\pi$
$132$	8.06180	+	22.4700i	0.701690	+	1.95576i
$133$	−0.0847853	−	0.395056i	−0.00735181	−	0.0342557i
$134$	7.24306			0.625705
$135$	11.6187	−	0.0719686i	0.999981	−	0.00619407i
$136$	2.81175	−	4.87010i	0.241106	−	0.417608i
$137$		−	16.6154i		−	1.41955i	−0.704429	−	0.709774i	$-0.748797\pi$
$137$		−	16.6154i		−	1.41955i	0.704429	−	0.709774i	$-0.251203\pi$
$138$	16.5012	−	19.4830i	1.40467	−	1.65851i
$139$	−4.95610	+	8.58422i	−0.420371	+	0.728104i	−0.995976	−	0.0896243i	$-0.971433\pi$
$139$	−4.95610	+	8.58422i	−0.420371	+	0.728104i	0.575605	+	0.817728i	$0.304767\pi$
$140$	11.4311	+	12.1488i	0.966107	+	1.02676i
$141$	−17.5127	−	14.8324i	−1.47484	−	1.24912i
$142$	−9.82931	−	5.67496i	−0.824858	−	0.476232i
$143$	−16.2981	−	9.40971i	−1.36291	−	0.786879i
$144$	3.91101	−	3.22101i	0.325918	−	0.268418i
$145$	0.604850	+	0.333292i	0.0502301	+	0.0276784i
$146$	−1.10285	−	1.91020i	−0.0912728	−	0.158089i
$147$	−8.41660	−	8.72702i	−0.694190	−	0.719792i
$148$	−5.09597	−	2.94216i	−0.418886	−	0.241844i
$149$	−19.5996			−1.60566			−0.802831	−	0.596207i	$-0.796674\pi$
$149$	−19.5996			−1.60566			−0.802831	+	0.596207i	$0.796674\pi$
$150$	17.6250	−	7.12979i	1.43907	−	0.582145i
$151$	5.02797			0.409170			0.204585	−	0.978849i	$-0.434416\pi$
$151$	5.02797			0.409170			0.204585	+	0.978849i	$0.434416\pi$
$152$	0.237987	−	0.137402i	0.0193033	−	0.0111448i
$153$	5.96026	+	7.23705i	0.481859	+	0.585081i
$154$	−19.0395	−	21.0620i	−1.53425	−	1.69722i
$155$	0.100232	+	0.0552308i	0.00805079	+	0.00443625i
$156$	3.35001	−	18.5019i	0.268216	−	1.48134i
$157$	13.3685	−	7.71831i	1.06692	−	0.615989i	0.139584	−	0.990210i	$-0.455423\pi$
$157$	13.3685	−	7.71831i	1.06692	−	0.615989i	0.927339	+	0.374222i	$0.122090\pi$
$158$	20.7159	−	11.9603i	1.64807	−	0.951514i
$159$	−0.244622	−	0.207183i	−0.0193998	−	0.0164307i
$160$	7.88493	−	14.3094i	0.623358	−	1.13126i
$161$	−5.45639	+	16.9062i	−0.430024	+	1.33240i
$162$	−6.41575	−	18.6877i	−0.504069	−	1.46824i
$163$	−7.20310	+	4.15871i	−0.564190	+	0.325735i	−0.754826	−	0.655925i	$-0.772279\pi$
$163$	−7.20310	+	4.15871i	−0.564190	+	0.325735i	0.190635	+	0.981661i	$0.438945\pi$
$164$	30.6170			2.39079
$165$	−17.6882	+	6.74770i	−1.37703	+	0.525308i
$166$	−4.70314			−0.365034
$167$	−6.62459	−	3.82471i	−0.512626	−	0.295965i	0.221286	−	0.975209i	$-0.428974\pi$
$167$	−6.62459	−	3.82471i	−0.512626	−	0.295965i	−0.733913	+	0.679244i	$0.762308\pi$
$168$	3.89034	−	7.27063i	0.300146	−	0.560942i
$169$	0.911393	+	1.57858i	0.0701072	+	0.121429i
$170$	13.4365	+	7.40395i	1.03053	+	0.567857i
$171$	0.0754122	+	0.451903i	0.00576691	+	0.0345579i
$172$	7.49177	+	4.32538i	0.571242	+	0.329807i
$173$	14.8804	+	8.59123i	1.13134	+	0.653179i	0.944271	−	0.329168i	$-0.106768\pi$
$173$	14.8804	+	8.59123i	1.13134	+	0.653179i	0.187068	+	0.982347i	$0.440102\pi$
$174$	0.209235	−	1.15559i	0.0158621	−	0.0876052i
$175$	−9.45151	+	9.25576i	−0.714467	+	0.699669i
$176$	−4.12772	+	7.14943i	−0.311139	+	0.538908i
$177$	−6.87609	−	19.1652i	−0.516839	−	1.44054i
$178$		−	10.9647i		−	0.821841i
$179$	9.25651	−	16.0327i	0.691864	−	1.19834i	−0.279362	−	0.960186i	$-0.590123\pi$
$179$	9.25651	−	16.0327i	0.691864	−	1.19834i	0.971226	−	0.238158i	$-0.0765436\pi$
$180$	−12.3137	−	14.3576i	−0.917811	−	1.07015i
$181$	−7.64653			−0.568362			−0.284181	−	0.958771i	$-0.591722\pi$
$181$	−7.64653			−0.568362			−0.284181	+	0.958771i	$0.591722\pi$
$182$	4.69250	+	21.8647i	0.347832	+	1.62072i
$183$	−3.87328	+	4.57320i	−0.286321	+	0.338061i
$184$	−12.0823			−0.890719
$185$	2.25209	−	4.08703i	0.165577	−	0.300485i
$186$	0.0346730	−	0.191497i	0.00254235	−	0.0140412i
$187$	−13.2295	−	7.63807i	−0.967438	−	0.558551i
$188$			37.3607i			2.72481i
$189$	9.07783	+	10.3244i	0.660315	+	0.750989i
$190$	0.387730	+	0.641637i	0.0281289	+	0.0465493i
$191$	7.14108	−	12.3687i	0.516711	−	0.894969i	−0.483101	−	0.875565i	$-0.660490\pi$
$191$	7.14108	−	12.3687i	0.516711	−	0.894969i	0.999812	−	0.0194046i	$-0.00617708\pi$
$192$	−21.5818	−	3.90768i	−1.55753	−	0.282012i
$193$	8.05800	−	4.65229i	0.580027	−	0.334879i	−0.181117	−	0.983462i	$-0.557971\pi$
$193$	8.05800	−	4.65229i	0.580027	−	0.334879i	0.761144	+	0.648583i	$0.224638\pi$
$194$	11.8628			0.851702
$195$	14.7227	+	2.36324i	1.05431	+	0.169235i
$196$	−1.98581	+	19.6374i	−0.141843	+	1.40267i
$197$			22.7250i			1.61909i	0.587058	+	0.809545i	$0.300286\pi$
$197$			22.7250i			1.61909i	−0.587058	+	0.809545i	$0.699714\pi$
$198$	20.4664	+	24.8507i	1.45448	+	1.76606i
$199$	−0.319464	+	0.553327i	−0.0226462	+	0.0392243i	−0.877126	−	0.480260i	$-0.840542\pi$
$199$	−0.319464	+	0.553327i	−0.0226462	+	0.0392243i	0.854480	+	0.519484i	$0.173876\pi$
$200$	−7.96511	−	4.18397i	−0.563219	−	0.295851i
$201$	5.37875	−	1.92979i	0.379387	−	0.136117i
$202$	−2.54059	−	1.46681i	−0.178755	−	0.103204i
$203$	0.171464	+	0.798936i	0.0120344	+	0.0560743i
$204$	2.71928	−	15.0184i	0.190388	−	1.05150i
$205$	0.484689	+	24.2754i	0.0338521	+	1.69547i
$206$	−8.51871	+	14.7548i	−0.593527	+	1.02802i
$207$	7.06297	−	18.8647i	0.490910	−	1.31119i
$208$	5.63112	−	3.25113i	0.390448	−	0.225425i
$209$	−0.373250	−	0.646487i	−0.0258182	−	0.0447185i
$210$	20.0428	+	10.2151i	1.38309	+	0.704910i
$211$	8.49264	−	14.7097i	0.584658	−	1.01266i	−0.410260	−	0.911968i	$-0.634562\pi$
$211$	8.49264	−	14.7097i	0.584658	−	1.01266i	0.994918	−	0.100688i	$-0.0321045\pi$
$212$			0.521864i			0.0358417i
$213$	−8.81132	−	1.59541i	−0.603741	−	0.109315i
$214$	−40.2493			−2.75138
$215$	−3.31088	+	6.00850i	−0.225800	+	0.409776i
$216$	−4.78610	+	8.03229i	−0.325653	+	0.546528i
$217$	0.0284138	+	0.132394i	0.00192886	+	0.00898750i
$218$	−22.5505	+	13.0195i	−1.52731	+	0.881795i
$219$	−1.32793	−	1.12469i	−0.0897331	−	0.0759995i
$220$	26.9925	+	14.8737i	1.81983	+	1.00279i
$221$	6.01599	+	10.4200i	0.404679	+	0.700925i
$222$	−7.80845	−	1.41382i	−0.524069	−	0.0948897i
$223$	−3.59338	+	2.07464i	−0.240631	+	0.138928i	−0.615467	−	0.788163i	$-0.711032\pi$
$223$	−3.59338	+	2.07464i	−0.240631	+	0.138928i	0.374836	+	0.927091i	$0.377699\pi$
$224$	18.9010	−	4.05645i	1.26288	−	0.271033i
$225$	11.1888	−	9.99051i	0.745921	−	0.666034i
$226$	8.19042	+	14.1862i	0.544819	+	0.943654i
$227$			13.4229i			0.890909i	0.895305	+	0.445455i	$0.146958\pi$
$227$			13.4229i			0.890909i	−0.895305	+	0.445455i	$0.853042\pi$
$228$	0.482032	−	0.569138i	0.0319233	−	0.0376921i
$229$	−17.8098			−1.17690			−0.588452	−	0.808532i	$-0.700263\pi$
$229$	−17.8098			−1.17690			−0.588452	+	0.808532i	$0.700263\pi$
$230$	−0.657987	−	32.9550i	−0.0433864	−	2.17299i
$231$	−19.7505	−	10.5680i	−1.29949	−	0.695325i
$232$	−0.481290	+	0.277873i	−0.0315982	+	0.0182432i
$233$	−7.65460	+	4.41939i	−0.501470	+	0.289524i	−0.729320	−	0.684172i	$-0.760164\pi$
$233$	−7.65460	+	4.41939i	−0.501470	+	0.289524i	0.227851	+	0.973696i	$0.426830\pi$
$234$	−4.17374	−	25.0109i	−0.272846	−	1.63501i
$235$	−29.6223	+	0.591445i	−1.93234	+	0.0385816i
$236$	−16.5734	+	28.7059i	−1.07883	+	1.86859i
$237$	12.1972	−	14.4013i	0.792291	−	0.935462i
$238$	3.80901	+	17.7481i	0.246901	+	1.15044i
$239$	7.99928	−	13.8552i	0.517430	−	0.896215i	−0.482365	−	0.875970i	$-0.660222\pi$
$239$	7.99928	−	13.8552i	0.517430	−	0.896215i	0.999795	−	0.0202449i	$-0.00644458\pi$
$240$	1.03667	−	6.45834i	0.0669169	−	0.416884i
$241$	24.8798			1.60265			0.801325	−	0.598229i	$-0.204129\pi$
$241$	24.8798			1.60265			0.801325	+	0.598229i	$0.204129\pi$
$242$	−24.5140	−	14.1531i	−1.57582	−	0.909799i
$243$	−9.74341	−	12.1682i	−0.625040	−	0.780593i
$244$	9.75621			0.624577
$245$	−15.6014	−	1.26362i	−0.996736	−	0.0807298i
$246$	38.8635	−	13.9435i	2.47785	−	0.889005i
$247$			0.587967i			0.0374115i
$248$	−0.0797560	+	0.0460471i	−0.00506451	+	0.00292400i
$249$	−3.49258	+	1.25307i	−0.221333	+	0.0794102i
$250$	10.9782	−	21.9530i	0.694321	−	1.38843i
$251$	11.2251			0.708520			0.354260	−	0.935147i	$-0.384733\pi$
$251$	11.2251			0.708520			0.354260	+	0.935147i	$0.384733\pi$
$252$	3.27445	−	22.1394i	0.206271	−	1.39465i
$253$			32.8213i			2.06346i
$254$	−0.677928	+	1.17421i	−0.0425370	+	0.0736762i
$255$	11.9507	+	1.91829i	0.748383	+	0.120128i
$256$	1.81178	+	3.13810i	0.113236	+	0.196131i
$257$		−	18.3838i		−	1.14675i	−0.819292	−	0.573376i	$-0.805633\pi$
$257$		−	18.3838i		−	1.14675i	0.819292	−	0.573376i	$-0.194367\pi$
$258$	11.4795	+	2.07852i	0.714682	+	0.129403i
$259$	5.39849	−	1.15860i	0.335446	−	0.0719919i
$260$	−12.5543	−	20.7756i	−0.778586	−	1.28845i
$261$	−0.152509	−	0.913898i	−0.00944004	−	0.0565689i
$262$	−6.77752	−	3.91300i	−0.418716	−	0.241746i
$263$			12.3509i			0.761586i	0.924660	+	0.380793i	$0.124349\pi$
$263$			12.3509i			0.761586i	−0.924660	+	0.380793i	$0.875651\pi$
$264$	2.71433	−	14.9910i	0.167055	−	0.922635i
$265$	−0.413772	+	0.00826147i	−0.0254178	+	0.000507498i
$266$	−0.272450	+	0.844167i	−0.0167050	+	0.0517592i
$267$	−2.92137	−	8.14248i	−0.178785	−	0.498312i
$268$	−8.05637	−	4.65135i	−0.492121	−	0.284126i
$269$	−6.81818	+	11.8094i	−0.415712	+	0.720034i	−0.995503	−	0.0947314i	$-0.969801\pi$
$269$	−6.81818	+	11.8094i	−0.415712	+	0.720034i	0.579791	+	0.814765i	$0.303134\pi$
$270$	−22.1691	−	12.6169i	−1.34917	−	0.767838i
$271$	3.80923	+	6.59779i	0.231394	+	0.400787i	0.958219	−	0.286037i	$-0.0923379\pi$
$271$	3.80923	+	6.59779i	0.231394	+	0.400787i	−0.726824	+	0.686823i	$0.759005\pi$
$272$	4.57091	−	2.63902i	0.277152	−	0.160014i
$273$	9.31017	+	14.9866i	0.563477	+	0.907032i
$274$	−18.2385	+	31.5899i	−1.10183	+	1.90842i
$275$	−11.3657	+	21.6371i	−0.685375	+	1.30476i
$276$	−30.8657	+	11.0740i	−1.85790	+	0.666579i
$277$			17.1616i			1.03114i	0.856848	+	0.515569i	$0.172420\pi$
$277$			17.1616i			1.03114i	−0.856848	+	0.515569i	$0.827580\pi$
$278$	18.8455	−	10.8805i	1.13028	−	0.652567i
$279$	−0.0252727	−	0.151445i	−0.00151303	−	0.00906677i
$280$	−2.44117	−	10.3619i	−0.145888	−	0.619241i
$281$	3.05170	+	5.28570i	0.182049	+	0.315319i	0.942578	−	0.333985i	$-0.108394\pi$
$281$	3.05170	+	5.28570i	0.182049	+	0.315319i	−0.760529	+	0.649304i	$0.775060\pi$
$282$	17.0147	+	47.4236i	1.01321	+	2.82403i
$283$	6.45607	−	3.72742i	0.383774	−	0.221572i	−0.295685	−	0.955285i	$-0.595548\pi$
$283$	6.45607	−	3.72742i	0.383774	−	0.221572i	0.679459	+	0.733714i	$0.262215\pi$
$284$	7.28869	+	12.6244i	0.432504	+	0.749120i
$285$	0.458885	+	0.373180i	0.0271820	+	0.0221053i
$286$	20.6578	+	35.7803i	1.22152	+	2.11574i
$287$	−21.3117	+	19.2653i	−1.25799	+	1.13719i
$288$	−21.6208	+	3.60801i	−1.27402	+	0.212604i
$289$	−3.61669	−	6.26428i	−0.212746	−	0.368487i
$290$	−0.784120	−	1.29760i	−0.0460451	−	0.0761980i
$291$	8.80943	−	3.16065i	0.516418	−	0.185281i
$292$			2.83293i			0.165784i
$293$	−0.500285	−	0.288839i	−0.0292269	−	0.0168742i	0.485315	−	0.874339i	$-0.338705\pi$
$293$	−0.500285	−	0.288839i	−0.0292269	−	0.0168742i	−0.514542	+	0.857465i	$0.672038\pi$
$294$	6.42252	+	25.8310i	0.374569	+	1.50649i
$295$	−23.0225	−	12.6861i	−1.34042	−	0.738615i
$296$	1.87761	+	3.25212i	0.109134	+	0.189026i
$297$	21.8196	+	13.0014i	1.26610	+	0.754415i
$298$	37.2637	+	21.5142i	2.15863	+	1.24628i
$299$	12.9256	−	22.3877i	0.747505	−	1.29472i
$300$	−24.1827	−	3.38803i	−1.39619	−	0.195608i
$301$	−7.93652	+	1.70330i	−0.457453	+	0.0981766i
$302$	−9.55940	−	5.51912i	−0.550082	−	0.317590i
$303$	−2.27747	−	0.412366i	−0.130837	−	0.0236898i
$304$	0.257922			0.0147928
$305$	0.154448	+	7.73543i	0.00884365	+	0.442930i
$306$	−3.38792	−	20.3019i	−0.193675	−	1.16058i
$307$		−	16.2016i		−	0.924673i	−0.886705	−	0.462336i	$-0.847011\pi$
$307$		−	16.2016i		−	0.924673i	0.886705	−	0.462336i	$-0.152989\pi$
$308$	7.65188	+	35.6539i	0.436006	+	2.03157i
$309$	−2.39487	+	13.2267i	−0.136240	+	0.752442i
$310$	−0.129939	−	0.215030i	−0.00738003	−	0.0122129i
$311$	−13.8228	−	23.9417i	−0.783817	−	1.35761i	−0.929704	−	0.368309i	$-0.879937\pi$
$311$	−13.8228	−	23.9417i	−0.783817	−	1.35761i	0.145887	−	0.989301i	$-0.453396\pi$
$312$	−7.75519	+	9.15659i	−0.439051	+	0.518390i
$313$	27.9701	+	16.1485i	1.58096	+	0.912769i	0.994719	+	0.102633i	$0.0327269\pi$
$313$	27.9701	+	16.1485i	1.58096	+	0.912769i	0.586243	+	0.810135i	$0.300606\pi$
$314$	−33.8891			−1.91247
$315$	17.6056	+	2.24574i	0.991962	+	0.126533i
$316$	−30.7228			−1.72829
$317$	−11.6588	−	6.73118i	−0.654821	−	0.378061i	0.135480	−	0.990780i	$-0.456742\pi$
$317$	−11.6588	−	6.73118i	−0.654821	−	0.378061i	−0.790301	+	0.612719i	$0.790076\pi$
$318$	0.237665	+	0.662425i	0.0133276	+	0.0371469i
$319$	0.754835	+	1.30741i	0.0422627	+	0.0732011i
$320$	−24.2341	+	14.6442i	−1.35472	+	0.818636i
$321$	−29.8894	+	10.7237i	−1.66826	+	0.598541i
$322$	28.9317	−	26.1535i	1.61230	−	1.45748i
$323$			0.477266i			0.0265558i
$324$	−4.86469	+	24.9062i	−0.270261	+	1.38368i
$325$	16.2737	−	10.2829i	0.902700	−	0.570391i
$326$	18.2598			1.01132
$327$	−13.2773	+	15.6766i	−0.734238	+	0.866919i
$328$	−16.9213	−	9.76951i	−0.934321	−	0.539431i
$329$	−23.5086	−	26.0058i	−1.29607	−	1.43375i
$330$	41.0365	+	6.58705i	2.25898	+	0.362605i
$331$	−3.12436	+	5.41154i	−0.171730	+	0.297445i	−0.939025	−	0.343849i	$-0.888269\pi$
$331$	−3.12436	+	5.41154i	−0.171730	+	0.297445i	0.767295	+	0.641295i	$0.221602\pi$
$332$	5.23125	+	3.02026i	0.287102	+	0.165758i
$333$	−6.17530	+	1.03052i	−0.338404	+	0.0564719i
$334$	8.39665	+	14.5434i	0.459444	+	0.795781i
$335$	3.56039	−	6.46132i	0.194525	−	0.353019i
$336$	6.57414	−	4.08406i	0.358649	−	0.222804i
$337$	12.7767	+	7.37664i	0.695992	+	0.401831i	0.805853	−	0.592116i	$-0.201707\pi$
$337$	12.7767	+	7.37664i	0.695992	+	0.401831i	−0.109861	+	0.993947i	$0.535040\pi$
$338$		−	4.00169i		−	0.217663i
$339$	9.86195	+	8.35259i	0.535628	+	0.453651i
$340$	−10.1906	−	16.8640i	−0.552664	−	0.914579i
$341$	0.125086	+	0.216655i	0.00677379	+	0.0117325i
$342$	0.352670	−	0.941957i	0.0190702	−	0.0509352i
$343$	−10.9743	−	14.9186i	−0.592554	−	0.805530i
$344$	−2.76035	−	4.78106i	−0.148828	−	0.257778i
$345$	−9.26893	−	24.2973i	−0.499022	−	1.30812i
$346$	−18.8609	−	32.6681i	−1.01397	−	1.75625i
$347$	12.0171	−	6.93808i	0.645113	−	0.372456i	−0.141469	−	0.989943i	$-0.545182\pi$
$347$	12.0171	−	6.93808i	0.645113	−	0.372456i	0.786581	+	0.617487i	$0.211849\pi$
$348$	−0.974829	+	1.15099i	−0.0522563	+	0.0616993i
$349$	−11.0094	−	19.0688i	−0.589319	−	1.02073i	−0.994322	−	0.106415i	$-0.966063\pi$
$349$	−11.0094	−	19.0688i	−0.589319	−	1.02073i	0.405003	−	0.914315i	$-0.367270\pi$
$350$	28.1295	−	7.22269i	1.50359	−	0.386069i
$351$	−9.76319	−	17.4613i	−0.521121	−	0.932013i
$352$	30.9304	−	17.8577i	1.64860	−	0.951818i
$353$		−	29.2431i		−	1.55645i	−0.627983	−	0.778227i	$-0.716119\pi$
$353$		−	29.2431i		−	1.55645i	0.627983	−	0.778227i	$-0.283881\pi$
$354$	−7.96415	+	43.9855i	−0.423290	+	2.33780i
$355$	−9.89415	+	5.97886i	−0.525127	+	0.317325i
$356$	−7.04133	+	12.1959i	−0.373190	+	0.646384i
$357$	7.55727	+	12.1650i	0.399973	+	0.643839i
$358$	−35.1978	+	20.3215i	−1.86026	+	1.07402i
$359$	12.7712	+	22.1204i	0.674040	+	1.16747i	0.976749	+	0.214388i	$0.0687757\pi$
$359$	12.7712	+	22.1204i	0.674040	+	1.16747i	−0.302709	+	0.953083i	$0.597891\pi$
$360$	2.22417	+	11.8643i	0.117224	+	0.625301i
$361$	9.48834	−	16.4343i	0.499386	−	0.864962i
$362$	14.5379	+	8.39348i	0.764097	+	0.441151i
$363$	−21.9751	−	3.97889i	−1.15339	−	0.208838i
$364$	8.82166	−	27.3333i	0.462380	−	1.43265i
$365$	−2.24615	+	0.0448472i	−0.117569	+	0.00234741i
$366$	12.3840	−	4.44314i	0.647322	−	0.232247i
$367$			13.4642i			0.702824i	0.936221	+	0.351412i	$0.114298\pi$
$367$			13.4642i			0.702824i	−0.936221	+	0.351412i	$0.885702\pi$
$368$	−9.82076	−	5.67002i	−0.511942	−	0.295570i
$369$	25.1453	−	20.7091i	1.30901	−	1.07807i
$370$	−8.76804	+	5.29837i	−0.455829	+	0.275449i
$371$	−0.328375	−	0.363256i	−0.0170484	−	0.0188593i
$372$	−0.161542	+	0.190733i	−0.00837556	+	0.00988907i
$373$			11.6514i			0.603289i	0.953421	+	0.301644i	$0.0975355\pi$
$373$			11.6514i			0.603289i	−0.953421	+	0.301644i	$0.902464\pi$
$374$	16.7684	+	29.0437i	0.867072	+	1.50181i
$375$	2.30345	−	19.2274i	0.118950	−	0.992900i
$376$	11.9213	−	20.6483i	0.614795	−	1.06486i
$377$		−	1.18907i		−	0.0612400i
$378$	−5.92626	−	29.5938i	−0.304814	−	1.52214i
$379$	28.7929			1.47899			0.739497	−	0.673160i	$-0.235064\pi$
$379$	28.7929			1.47899			0.739497	+	0.673160i	$0.235064\pi$
$380$	−0.0192211	−	0.962679i	−0.000986021	−	0.0493844i
$381$	−0.190587	+	1.05260i	−0.00976404	+	0.0539261i
$382$	−27.1539	+	15.6773i	−1.38932	+	0.802121i
$383$		−	4.43919i		−	0.226832i	−0.993548	−	0.113416i	$-0.963821\pi$
$383$		−	4.43919i		−	0.226832i	0.993548	−	0.113416i	$-0.0361793\pi$
$384$	17.4287	+	14.7613i	0.889404	+	0.753282i
$385$	−28.1479	+	6.63139i	−1.43455	+	0.337967i
$386$	−20.4270			−1.03971
$387$	9.07854	−	1.51500i	0.461488	−	0.0770117i
$388$	−13.1949	−	7.61808i	−0.669870	−	0.386749i
$389$	17.0337			0.863641			0.431821	−	0.901959i	$-0.357871\pi$
$389$	17.0337			0.863641			0.431821	+	0.901959i	$0.357871\pi$
$390$	−25.3973	−	20.6539i	−1.28604	−	1.04585i
$391$	10.4920	−	18.1726i	0.530602	−	0.919029i
$392$	7.36355	−	10.2195i	0.371916	−	0.516161i
$393$	−6.07559	−	1.10007i	−0.306473	−	0.0554910i
$394$	24.9449	−	43.2058i	1.25671	−	2.17668i
$395$	−0.486364	−	24.3593i	−0.0244716	−	1.22565i
$396$	−6.80596	−	40.7843i	−0.342012	−	2.04949i
$397$	9.16769	−	5.29297i	0.460113	−	0.265647i	−0.251979	−	0.967733i	$-0.581081\pi$
$397$	9.16769	−	5.29297i	0.460113	−	0.265647i	0.712092	+	0.702086i	$0.247748\pi$
$398$	1.21476	−	0.701341i	0.0608903	−	0.0351550i
$399$	0.0225910	+	0.699474i	0.00113097	+	0.0350175i
$400$	−4.51076	−	7.13871i	−0.225538	−	0.356936i
$401$	−3.00692			−0.150159			−0.0750793	−	0.997178i	$-0.523921\pi$
$401$	−3.00692			−0.150159			−0.0750793	+	0.997178i	$0.523921\pi$
$402$	−12.3446	−	2.23516i	−0.615694	−	0.111480i
$403$		−	0.197044i		−	0.00981545i
$404$	1.88392	+	3.26304i	0.0937283	+	0.162342i
$405$	−19.8245	−	3.46280i	−0.985085	−	0.172068i
$406$	0.550984	−	1.70719i	0.0273449	−	0.0847262i
$407$	8.83432	−	5.10049i	0.437901	−	0.252822i
$408$	−6.29506	+	7.43261i	−0.311652	+	0.367969i
$409$	9.84976	+	17.0603i	0.487040	+	0.843577i	0.999889	−	0.0149014i	$-0.00474343\pi$
$409$	9.84976	+	17.0603i	0.487040	+	0.843577i	−0.512849	+	0.858479i	$0.671410\pi$
$410$	25.7252	−	46.6855i	1.27048	−	2.30563i
$411$	−5.12740	+	28.3183i	−0.252916	+	1.39684i
$412$	18.9505	−	10.9411i	0.933626	−	0.539029i
$413$	−6.52646	−	30.4100i	−0.321146	−	1.49638i
$414$	−34.1359	+	28.1135i	−1.67769	+	1.38170i
$415$	−2.31187	+	4.19553i	−0.113485	+	0.205950i
$416$	−28.1306			−1.37922
$417$	11.0959	−	13.1010i	0.543369	−	0.641558i
$418$			1.63884i			0.0801584i
$419$	−4.09021	+	7.08445i	−0.199820	+	0.346098i	−0.948470	−	0.316867i	$-0.897369\pi$
$419$	−4.09021	+	7.08445i	−0.199820	+	0.346098i	0.748650	+	0.662965i	$0.230702\pi$
$420$	−15.7335	−	24.2333i	−0.767715	−	1.18246i
$421$	−9.21363	−	15.9585i	−0.449045	−	0.777768i	0.549279	−	0.835639i	$-0.314902\pi$
$421$	−9.21363	−	15.9585i	−0.449045	−	0.777768i	−0.998324	+	0.0578705i	$0.981569\pi$
$422$	−32.2932	+	18.6445i	−1.57201	+	0.907599i
$423$	25.2704	+	30.6838i	1.22869	+	1.49190i
$424$	0.166520	−	0.288421i	0.00808693	−	0.0140070i
$425$	13.2097	−	8.34684i	0.640764	−	0.404881i
$426$	15.0012	+	12.7053i	0.726812	+	0.615574i
$427$	−6.79105	+	6.13895i	−0.328642	+	0.297085i
$428$	44.7688	+	25.8473i	2.16398	+	1.24938i
$429$	24.8737	+	21.0668i	1.20091	+	1.01711i
$430$	12.8902	−	7.78934i	0.621622	−	0.375635i
$431$	9.78325	−	16.9451i	0.471242	−	0.816216i	−0.528216	−	0.849110i	$-0.677139\pi$
$431$	9.78325	−	16.9451i	0.471242	−	0.816216i	0.999459	+	0.0328939i	$0.0104724\pi$
$432$	−7.65967	+	4.28279i	−0.368526	+	0.206056i
$433$		−	0.553283i		−	0.0265891i	−0.999912	−	0.0132945i	$-0.995768\pi$
$433$		−	0.553283i		−	0.0265891i	0.999912	−	0.0132945i	$-0.00423191\pi$
$434$	0.0913053	−	0.282903i	0.00438279	−	0.0135798i
$435$	−0.928018	−	0.754695i	−0.0444951	−	0.0361848i
$436$	33.4436			1.60166
$437$	0.888043	−	0.512712i	0.0424808	−	0.0245263i
$438$	1.29016	+	3.59596i	0.0616463	+	0.171822i
$439$	−15.0513	+	26.0697i	−0.718361	+	1.24424i	0.243288	+	0.969954i	$0.421774\pi$
$439$	−15.0513	+	26.0697i	−0.718361	+	1.24424i	−0.961649	+	0.274283i	$0.911559\pi$
$440$	−10.1721	−	16.8333i	−0.484935	−	0.802497i
$441$	11.6516	+	17.4711i	0.554840	+	0.831957i
$442$		−	26.4147i		−	1.25642i
$443$	−12.6363	−	7.29560i	−0.600371	−	0.346624i	0.168817	−	0.985647i	$-0.446005\pi$
$443$	−12.6363	−	7.29560i	−0.600371	−	0.346624i	−0.769187	+	0.639023i	$0.779339\pi$
$444$	7.77732	+	6.58702i	0.369095	+	0.312606i
$445$	−9.78131	−	5.38981i	−0.463678	−	0.255502i
$446$	9.10921			0.431333
$447$	33.4044	+	6.04831i	1.57997	+	0.286075i
$448$	−31.8834	−	10.2902i	−1.50635	−	0.486165i
$449$	0.891063			0.0420519			0.0210259	−	0.999779i	$-0.493307\pi$
$449$	0.891063			0.0420519			0.0210259	+	0.999779i	$0.493307\pi$
$450$	−32.2391	+	6.71262i	−1.51977	+	0.316436i
$451$	−26.5387	+	45.9663i	−1.24966	+	2.16447i
$452$		−	21.0389i		−	0.989588i
$453$	−8.56936	−	1.55160i	−0.402624	−	0.0729004i
$454$	14.7341	−	25.5202i	0.691506	−	1.19772i
$455$	21.8115	+	6.56175i	1.02254	+	0.307620i
$456$	−0.448012	+	0.160738i	−0.0209801	+	0.00752726i
$457$	7.50531	+	4.33319i	0.351084	+	0.202698i	0.665162	−	0.746699i	$-0.268362\pi$
$457$	7.50531	+	4.33319i	0.351084	+	0.202698i	−0.314079	+	0.949397i	$0.601696\pi$
$458$	33.8608	+	19.5495i	1.58221	+	0.913490i
$459$	−7.92500	−	14.1737i	−0.369907	−	0.661571i
$460$	−20.4312	+	37.0780i	−0.952608	+	1.72877i
$461$	4.54429	+	7.87094i	0.211649	+	0.366586i	0.952231	−	0.305380i	$-0.0987834\pi$
$461$	4.54429	+	7.87094i	0.211649	+	0.366586i	−0.740582	+	0.671966i	$0.765450\pi$
$462$	25.9502	+	41.7723i	1.20731	+	1.94342i
$463$	10.5116	+	6.06889i	0.488517	+	0.282045i	0.723959	−	0.689843i	$-0.242320\pi$
$463$	10.5116	+	6.06889i	0.488517	+	0.282045i	−0.235442	+	0.971888i	$0.575654\pi$
$464$	−0.521604			−0.0242148
$465$	−0.153785	−	0.125063i	−0.00713159	−	0.00579965i
$466$	19.4044			0.898890
$467$	4.83631	−	2.79225i	0.223798	−	0.129210i	−0.383910	−	0.923371i	$-0.625423\pi$
$467$	4.83631	−	2.79225i	0.223798	−	0.129210i	0.607708	+	0.794161i	$0.292089\pi$
$468$	−11.4191	+	30.4997i	−0.527848	+	1.40985i
$469$	8.53463	−	1.83167i	0.394093	−	0.0845785i
$470$	56.9684	+	31.3914i	2.62776	+	1.44798i
$471$	−25.1663	+	9.02919i	−1.15960	+	0.416043i
$472$	18.3194	−	10.5767i	0.843218	−	0.486832i
$473$	−12.9877	+	7.49843i	−0.597173	+	0.344778i
$474$	−38.9978	+	13.9917i	−1.79123	+	0.642659i
$475$	0.762978	−	0.0304798i	0.0350078	−	0.00139851i
$476$	7.16074	−	22.1870i	0.328212	−	1.01694i
$477$	0.352984	+	0.428599i	0.0161620	+	0.0196242i
$478$	−30.4172	+	17.5614i	−1.39125	+	0.803238i
$479$	12.4714			0.569834			0.284917	−	0.958552i	$-0.408034\pi$
$479$	12.4714			0.569834			0.284917	+	0.958552i	$0.408034\pi$
$480$	−17.8544	+	21.9548i	−0.814937	+	1.00210i
$481$	−8.03463			−0.366348
$482$	−47.3027	−	27.3102i	−2.15458	−	1.24395i
$483$	14.5167	−	27.1302i	0.660532	−	1.23446i
$484$	18.1778	+	31.4848i	0.826261	+	1.43113i
$485$	5.83129	−	10.5825i	0.264785	−	0.480526i
$486$	5.16772	+	33.8300i	0.234413	+	1.53456i
$487$	33.1059	+	19.1137i	1.50017	+	0.866125i	1.00000		0.000198459i	$6.31715e-5\pi$
$487$	33.1059	+	19.1137i	1.50017	+	0.866125i	0.500172	+	0.865926i	$0.333270\pi$
$488$	−5.39202	−	3.11309i	−0.244085	−	0.140923i
$489$	13.5599	−	4.86503i	0.613199	−	0.220004i
$490$	28.2750	+	19.5279i	1.27733	+	0.882179i
$491$	−12.6344	+	21.8835i	−0.570185	+	0.987589i	0.426362	+	0.904553i	$0.359795\pi$
$491$	−12.6344	+	21.8835i	−0.570185	+	0.987589i	−0.996547	+	0.0830360i	$0.973538\pi$
$492$	−52.1817	−	9.44820i	−2.35253	−	0.425958i
$493$		−	0.965191i		−	0.0434700i
$494$	0.645403	−	1.11787i	0.0290380	−	0.0502954i
$495$	32.2290	−	6.04190i	1.44859	−	0.271563i
$496$	−0.0864365			−0.00388112
$497$	−13.0172	−	4.20122i	−0.583901	−	0.188450i
$498$	8.01574	+	1.45136i	0.359194	+	0.0650368i
$499$	26.7264			1.19644			0.598220	−	0.801332i	$-0.295875\pi$
$499$	26.7264			1.19644			0.598220	+	0.801332i	$0.295875\pi$
$500$	−26.3087	+	17.3682i	−1.17656	+	0.776728i
$501$	10.1103	+	8.56290i	0.451693	+	0.382562i
$502$	−21.3416	−	12.3216i	−0.952523	−	0.549939i
$503$			3.24713i			0.144782i	0.997376	+	0.0723912i	$0.0230630\pi$
$503$			3.24713i			0.144782i	−0.997376	+	0.0723912i	$0.976937\pi$
$504$	−8.87412	+	11.1911i	−0.395285	+	0.498491i
$505$	−2.55735	+	1.54536i	−0.113801	+	0.0687677i
$506$	36.0275	−	62.4014i	1.60162	−	2.77408i
$507$	−1.06618	−	2.97168i	−0.0473509	−	0.131977i
$508$	1.50810	−	0.870704i	0.0669113	−	0.0386312i
$509$	−2.55254			−0.113139			−0.0565697	−	0.998399i	$-0.518016\pi$
$509$	−2.55254			−0.113139			−0.0565697	+	0.998399i	$0.518016\pi$
$510$	−20.6156	−	16.7653i	−0.912873	−	0.742378i
$511$	−1.78258	−	1.97193i	−0.0788566	−	0.0872330i
$512$			18.4180i			0.813969i
$513$	0.0109263	−	0.793467i	0.000482409	−	0.0350324i
$514$	−20.1797	+	34.9522i	−0.890086	+	1.54167i
$515$	8.97490	+	14.8522i	0.395481	+	0.654465i
$516$	−11.4337	−	9.68382i	−0.503342	−	0.426306i
$517$	−56.0908	−	32.3840i	−2.46687	−	1.42425i
$518$	−11.5356	−	3.72305i	−0.506846	−	0.163582i
$519$	−22.7101	−	19.2344i	−0.996864	−	0.844295i
$520$	0.309239	+	15.4881i	0.0135610	+	0.679198i
$521$	5.60787	−	9.71312i	0.245685	−	0.425540i	−0.716639	−	0.697445i	$-0.754320\pi$
$521$	5.60787	−	9.71312i	0.245685	−	0.425540i	0.962324	+	0.271905i	$0.0876537\pi$
$522$	−0.713216	+	1.90495i	−0.0312166	+	0.0833775i
$523$	−14.1845	+	8.18941i	−0.620244	+	0.358098i	−0.776964	−	0.629545i	$-0.783241\pi$
$523$	−14.1845	+	8.18941i	−0.620244	+	0.358098i	0.156720	+	0.987643i	$0.449908\pi$
$524$	5.02571	+	8.70478i	0.219549	+	0.380270i
$525$	18.9648	−	12.8583i	0.827693	−	0.561181i
$526$	13.5573	−	23.4820i	0.591128	−	1.02386i
$527$		−	0.159945i		−	0.00696731i
$528$	9.24131	−	10.9113i	0.402176	−	0.474852i
$529$	−22.0847			−0.960206
$530$	0.795750	+	0.438484i	0.0345652	+	0.0190465i
$531$	5.80495	+	34.7858i	0.251914	+	1.50958i
$532$	0.845150	−	0.763996i	0.0366419	−	0.0331234i
$533$	36.2046	−	20.9027i	1.56819	−	0.905397i
$534$	−3.38364	+	18.6876i	−0.146424	+	0.808692i
$535$	−19.7849	+	35.9052i	−0.855376	+	1.55232i
$536$	2.96838	+	5.14138i	0.128214	+	0.222074i
$537$	−20.7238	+	24.4687i	−0.894299	+	1.05590i
$538$	25.9261	−	14.9684i	1.11775	−	0.645334i
$539$	−27.7610	−	20.0029i	−1.19575	−	0.861588i
$540$	16.5561	+	28.2701i	0.712461	+	1.21655i
$541$	−11.4345	−	19.8051i	−0.491608	−	0.851490i	0.508345	−	0.861153i	$-0.330257\pi$
$541$	−11.4345	−	19.8051i	−0.491608	−	0.851490i	−0.999953	+	0.00966348i	$0.996924\pi$
$542$		−	16.7253i		−	0.718415i
$543$	13.0323	+	2.35967i	0.559268	+	0.101263i
$544$	−22.8342			−0.979010
$545$	0.529436	+	26.5165i	0.0226785	+	1.13584i
$546$	−1.25032	−	38.7129i	−0.0535087	−	1.65676i
$547$	30.6061	−	17.6704i	1.30862	−	0.755534i	0.326757	−	0.945109i	$-0.394044\pi$
$547$	30.6061	−	17.6704i	1.30862	−	0.755534i	0.981866	+	0.189575i	$0.0607109\pi$
$548$	40.5729	−	23.4248i	1.73319	−	1.00066i
$549$	8.01264	−	6.59902i	0.341971	−	0.281639i
$550$	45.3596	−	28.6615i	1.93414	−	1.22213i
$551$	0.0235830	−	0.0408470i	0.00100467	−	0.00174014i
$552$	20.5923	+	3.72852i	0.876468	+	0.158696i
$553$	21.3854	−	19.3319i	0.909399	−	0.822075i
$554$	18.8380	−	32.6284i	0.800349	−	1.38625i
$555$	−5.09955	+	6.27071i	−0.216464	+	0.266177i
$556$	−27.9489			−1.18530
$557$	−15.7684	−	9.10389i	−0.668129	−	0.385744i	0.127239	−	0.991872i	$-0.459389\pi$
$557$	−15.7684	−	9.10389i	−0.668129	−	0.385744i	−0.795367	+	0.606128i	$0.792722\pi$
$558$	−0.118189	+	0.315675i	−0.00500335	+	0.0133636i
$559$	11.8120			0.499595
$560$	2.87842	−	9.56797i	0.121635	−	0.404321i
$561$	20.1905	+	17.1004i	0.852445	+	0.721979i
$562$		−	13.3992i		−	0.565212i
$563$	−26.2861	+	15.1763i	−1.10783	+	0.639604i	−0.938266	−	0.345916i	$-0.887568\pi$
$563$	−26.2861	+	15.1763i	−1.10783	+	0.639604i	−0.169561	+	0.985520i	$0.554235\pi$
$564$	11.5292	−	63.6752i	0.485469	−	2.68121i
$565$	16.6812	−	0.333061i	0.701783	−	0.0140120i
$566$	−16.3661			−0.687919
$567$	−12.2857	−	20.3976i	−0.515949	−	0.856619i
$568$		−	9.30293i		−	0.390342i
$569$	−0.358831	+	0.621513i	−0.0150430	+	0.0260552i	−0.873449	−	0.486916i	$-0.838122\pi$
$569$	−0.358831	+	0.621513i	−0.0150430	+	0.0260552i	0.858406	+	0.512971i	$0.171455\pi$
$570$	−0.462818	−	1.21322i	−0.0193853	−	0.0508161i
$571$	4.72169	+	8.17821i	0.197597	+	0.342247i	0.947749	−	0.319018i	$-0.103353\pi$
$571$	4.72169	+	8.17821i	0.197597	+	0.342247i	−0.750152	+	0.661265i	$0.770020\pi$
$572$		−	53.0641i		−	2.21872i
$573$	−15.9877	+	18.8768i	−0.667897	+	0.788590i
$574$	61.6661	−	13.2345i	2.57389	−	0.552397i
$575$	−29.7216	−	15.6124i	−1.23948	−	0.651080i
$576$	35.5769	+	13.3200i	1.48237	+	0.555001i
$577$	−26.4339	−	15.2616i	−1.10046	−	0.635348i	−0.164115	−	0.986441i	$-0.552477\pi$
$577$	−26.4339	−	15.2616i	−1.10046	−	0.635348i	−0.936341	+	0.351093i	$0.885810\pi$
$578$			15.8799i			0.660518i
$579$	−15.1692	+	5.44243i	−0.630411	+	0.226180i
$580$	0.0388715	+	1.94686i	0.00161405	+	0.0808389i
$581$	−5.54180	+	1.18936i	−0.229913	+	0.0493428i
$582$	−20.2183	−	3.66079i	−0.838075	−	0.151745i
$583$	−0.783491	−	0.452349i	−0.0324489	−	0.0187344i
$584$	0.903952	−	1.56569i	0.0374058	−	0.0647887i
$585$	−24.3631	−	8.57107i	−1.00729	−	0.354370i
$586$	0.634109	+	1.09831i	0.0261948	+	0.0453708i
$587$	−25.8996	+	14.9531i	−1.06899	+	0.617182i	−0.927906	−	0.372815i	$-0.878393\pi$
$587$	−25.8996	+	14.9531i	−1.06899	+	0.617182i	−0.141085	+	0.989997i	$0.545059\pi$
$588$	9.44446	−	32.8559i	0.389483	−	1.35496i
$589$	0.00390801	−	0.00676888i	0.000161027	−	0.000278907i
$590$	29.8460	+	49.3909i	1.22874	+	2.03339i
$591$	7.01279	−	38.7311i	0.288468	−	1.59319i
$592$			3.52453i			0.144857i
$593$	−2.65336	+	1.53192i	−0.108960	+	0.0629082i	−0.553490	−	0.832856i	$-0.686704\pi$
$593$	−2.65336	+	1.53192i	−0.108960	+	0.0629082i	0.444530	+	0.895764i	$0.353371\pi$
$594$	−27.2129	−	48.6698i	−1.11656	−	1.99694i
$595$	17.7049	+	5.32632i	0.725829	+	0.218358i
$596$	−27.6320	−	47.8600i	−1.13185	−	1.96042i
$597$	0.715227	−	0.844473i	0.0292723	−	0.0345620i
$598$	−49.1494	+	28.3764i	−2.00987	+	1.16040i
$599$	20.2649	+	35.0998i	0.828000	+	1.43414i	0.899605	+	0.436704i	$0.143854\pi$
$599$	20.2649	+	35.0998i	0.828000	+	1.43414i	−0.0716055	+	0.997433i	$0.522812\pi$
$600$	12.2841	+	9.58888i	0.501497	+	0.391464i
$601$	9.61495	+	16.6536i	0.392202	+	0.679314i	0.992740	−	0.120283i	$-0.0383801\pi$
$601$	9.61495	+	16.6536i	0.392202	+	0.679314i	−0.600538	+	0.799597i	$0.705047\pi$
$602$	16.9590	+	5.47340i	0.691195	+	0.223079i
$603$	−9.76272	+	1.62917i	−0.397569	+	0.0663451i
$604$	7.08855	+	12.2777i	0.288429	+	0.499573i
$605$	−24.6757	+	14.9111i	−1.00321	+	0.606221i
$606$	3.87738	+	3.28395i	0.157508	+	0.133401i
$607$		−	11.4201i		−	0.463526i	−0.972772	−	0.231763i	$-0.925551\pi$
$607$		−	11.4201i		−	0.463526i	0.972772	−	0.231763i	$-0.0744495\pi$
$608$	−0.966347	−	0.557921i	−0.0391905	−	0.0226267i
$609$	−0.0456866	−	1.41457i	−0.00185132	−	0.0573212i
$610$	8.19743	−	14.8765i	0.331904	−	0.602332i
$611$	25.5067	+	44.1789i	1.03189	+	1.78729i
$612$	−9.26914	+	24.7573i	−0.374683	+	1.00075i
$613$	1.81300	+	1.04674i	0.0732265	+	0.0422774i	0.536166	−	0.844112i	$-0.319872\pi$
$613$	1.81300	+	1.04674i	0.0732265	+	0.0422774i	−0.462940	+	0.886390i	$0.653205\pi$
$614$	−17.7842	+	30.8032i	−0.717713	+	1.24312i
$615$	6.66515	−	41.5231i	0.268765	−	1.67437i
$616$	7.14770	−	22.1467i	0.287989	−	0.892314i
$617$	−7.26007	−	4.19160i	−0.292279	−	0.168748i	0.346690	−	0.937980i	$-0.387306\pi$
$617$	−7.26007	−	4.19160i	−0.292279	−	0.168748i	−0.638969	+	0.769232i	$0.720639\pi$
$618$	19.0720	−	22.5184i	0.767189	−	0.905824i
$619$	−38.8020			−1.55958			−0.779792	−	0.626039i	$-0.784675\pi$
$619$	−38.8020			−1.55958			−0.779792	+	0.626039i	$0.784675\pi$
$620$	0.00644151	+	0.322620i	0.000258697	+	0.0129567i
$621$	−17.8592	+	29.9723i	−0.716665	+	1.20275i
$622$			60.6921i			2.43353i
$623$	−2.77282	−	12.9200i	−0.111091	−	0.517627i
$624$	−10.6006	+	3.80330i	−0.424364	+	0.152254i
$625$	−14.1872	−	20.5845i	−0.567489	−	0.823381i
$626$	−35.4520	−	61.4046i	−1.41695	−	2.45422i
$627$	0.436642	+	1.21702i	0.0174378	+	0.0486029i
$628$	37.6945	+	21.7629i	1.50417	+	0.868435i
$629$	−6.52189			−0.260045
$630$	−31.0074	−	23.5951i	−1.23537	−	0.940051i
$631$	−44.4178			−1.76824			−0.884122	−	0.467257i	$-0.845242\pi$
$631$	−44.4178			−1.76824			−0.884122	+	0.467257i	$0.845242\pi$
$632$	16.9798	+	9.80327i	0.675418	+	0.389953i
$633$	−19.0136	+	22.4495i	−0.755725	+	0.892288i
$634$	14.7774	+	25.5953i	0.586887	+	1.01652i
$635$	0.714232	+	1.18195i	0.0283434	+	0.0469043i
$636$	0.161044	−	0.889432i	0.00638579	−	0.0352683i
$637$	11.0585	+	24.5769i	0.438155	+	0.973773i
$638$		−	3.31428i		−	0.131214i
$639$	14.5251	+	5.43823i	0.574605	+	0.215133i
$640$	29.4801	−	0.588608i	1.16530	−	0.0232668i
$641$	−45.5889			−1.80065			−0.900326	−	0.435216i	$-0.856672\pi$
$641$	−45.5889			−1.80065			−0.900326	+	0.435216i	$0.856672\pi$
$642$	68.5984	+	12.4207i	2.70736	+	0.490204i
$643$	17.7614	+	10.2546i	0.700442	+	0.404401i	0.807512	−	0.589851i	$-0.200813\pi$
$643$	17.7614	+	10.2546i	0.700442	+	0.404401i	−0.107070	+	0.994252i	$0.534147\pi$
$644$	−48.9757	+	10.5109i	−1.92991	+	0.414189i
$645$	7.49703	−	9.21880i	0.295195	−	0.362990i
$646$	0.523888	−	0.907400i	0.0206121	−	0.0357012i
$647$	0.510132	+	0.294525i	0.0200554	+	0.0115790i	0.509994	−	0.860178i	$-0.329648\pi$
$647$	0.510132	+	0.294525i	0.0200554	+	0.0115790i	−0.489939	+	0.871757i	$0.662981\pi$
$648$	10.6359	−	12.2128i	0.417816	−	0.479764i
$649$	−28.7314	−	49.7642i	−1.12781	−	1.95342i
$650$	−42.2276	+	1.68693i	−1.65630	+	0.0661667i
$651$	−0.00757087	−	0.234413i	−0.000296726	−	0.00918736i
$652$	−20.3102	−	11.7261i	−0.795409	−	0.459230i
$653$			18.3153i			0.716735i	0.933581	+	0.358367i	$0.116666\pi$
$653$			18.3153i			0.716735i	−0.933581	+	0.358367i	$0.883334\pi$
$654$	42.4515	−	15.2308i	1.65998	−	0.595570i
$655$	−6.82222	+	4.12255i	−0.266566	+	0.161081i
$656$	−9.16933	−	15.8817i	−0.358002	−	0.620078i
$657$	1.91617	+	2.32664i	0.0747568	+	0.0907710i
$658$	16.1495	+	75.2485i	0.629573	+	2.93349i
$659$	8.14390	+	14.1056i	0.317241	+	0.549478i	0.979911	−	0.199434i	$-0.0639102\pi$
$659$	8.14390	+	14.1056i	0.317241	+	0.549478i	−0.662670	+	0.748911i	$0.730577\pi$
$660$	−41.4144	−	33.6795i	−1.61205	−	1.31097i
$661$	4.38448	+	7.59414i	0.170536	+	0.295378i	0.938608	−	0.344987i	$-0.112117\pi$
$661$	4.38448	+	7.59414i	0.170536	+	0.295378i	−0.768071	+	0.640365i	$0.778783\pi$
$662$	11.8803	−	6.85911i	0.461742	−	0.266587i
$663$	−7.03774	−	19.6157i	−0.273323	−	0.761811i
$664$	−1.92746	−	3.33845i	−0.0747998	−	0.129557i
$665$	0.619131	+	0.658002i	0.0240089	+	0.0255162i
$666$	12.8719	+	4.81927i	0.498778	+	0.186743i
$667$	−1.79592	+	1.03687i	−0.0695382	+	0.0401479i
$668$		−	21.5687i		−	0.834517i
$669$	6.76456	−	2.42700i	0.261533	−	0.0938331i
$670$	−13.8617	+	8.37636i	−0.535523	+	0.323607i
$671$	−8.45663	+	14.6473i	−0.326465	+	0.565453i
$672$	−33.4655	+	1.08084i	−1.29096	+	0.0416944i
$673$	44.7886	−	25.8587i	1.72647	−	0.996780i	0.823148	−	0.567827i	$-0.192216\pi$
$673$	44.7886	−	25.8587i	1.72647	−	0.996780i	0.903327	−	0.428953i	$-0.141117\pi$
$674$	−16.1945	−	28.0496i	−0.623787	−	1.08043i
$675$	−22.1525	+	13.5744i	−0.852652	+	0.522480i
$676$	−2.56981	+	4.45104i	−0.0988387	+	0.171194i
$677$	13.7209	+	7.92174i	0.527335	+	0.304457i	0.739931	−	0.672683i	$-0.234858\pi$
$677$	13.7209	+	7.92174i	0.527335	+	0.304457i	−0.212595	+	0.977140i	$0.568192\pi$
$678$	−9.58148	−	26.7057i	−0.367975	−	1.02562i
$679$	13.9782	−	2.99994i	0.536434	−	0.115127i
$680$	0.251016	+	12.5720i	0.00962604	+	0.482116i
$681$	4.14222	−	22.8772i	0.158730	−	0.876655i
$682$		−	0.549220i		−	0.0210307i
$683$	12.0225	+	6.94117i	0.460027	+	0.265597i	0.712056	−	0.702123i	$-0.247764\pi$
$683$	12.0225	+	6.94117i	0.460027	+	0.265597i	−0.252029	+	0.967720i	$0.581098\pi$
$684$	−0.997178	+	0.821251i	−0.0381280	+	0.0314013i
$685$	19.2152	+	31.7983i	0.734174	+	1.21495i
$686$	4.48881	+	40.4103i	0.171384	+	1.54287i
$687$	30.3539	+	5.49599i	1.15807	+	0.209685i
$688$		−	5.18154i		−	0.197544i
$689$	0.356285	+	0.617103i	0.0135734	+	0.0235098i
$690$	−9.04825	+	56.3695i	−0.344461	+	2.14595i
$691$	16.5481	−	28.6622i	0.629521	−	1.09036i	−0.358127	−	0.933673i	$-0.616585\pi$
$691$	16.5481	−	28.6622i	0.629521	−	1.09036i	0.987648	−	0.156689i	$-0.0500822\pi$
$692$			48.4485i			1.84173i
$693$	30.4004	+	24.1064i	1.15481	+	0.915725i
$694$	−30.4633			−1.15637
$695$	−0.442451	−	22.1599i	−0.0167831	−	0.840574i
$696$	0.906030	−	0.325066i	0.0343430	−	0.0123216i
$697$	29.3881	−	16.9672i	1.11315	−	0.642679i
$698$			48.3393i			1.82967i
$699$	14.4098	−	5.16997i	0.545030	−	0.195546i
$700$	−35.9265	−	10.0305i	−1.35789	−	0.379118i
$701$	40.9648			1.54722			0.773609	−	0.633663i	$-0.218449\pi$
$701$	40.9648			1.54722			0.773609	+	0.633663i	$0.218449\pi$
$702$	−0.604726	+	43.9150i	−0.0228239	+	1.65747i
$703$	−0.276007	−	0.159353i	−0.0104098	−	0.00601010i
$704$	−61.8976			−2.33285
$705$	50.6689	+	8.13321i	1.90830	+	0.306314i
$706$	−32.0997	+	55.5983i	−1.20809	+	2.09247i
$707$	−3.36456	−	1.08589i	−0.126537	−	0.0408392i
$708$	37.1050	−	43.8101i	1.39449	−	1.64649i
$709$	−3.29538	+	5.70776i	−0.123761	+	0.214360i	−0.921248	−	0.388976i	$-0.872829\pi$
$709$	−3.29538	+	5.70776i	−0.123761	+	0.214360i	0.797487	+	0.603336i	$0.206162\pi$
$710$	25.3741	−	0.506626i	0.952274	−	0.0190133i
$711$	−25.2322	+	20.7806i	−0.946282	+	0.779335i
$712$	7.78315	−	4.49360i	0.291686	−	0.168405i
$713$	−0.297607	+	0.171824i	−0.0111455	+	0.00643484i
$714$	−1.01491	−	31.4241i	−0.0379821	−	1.17602i
$715$	42.0731	−	0.840042i	1.57344	−	0.0314158i
$716$	52.2002			1.95081
$717$	−17.9091	+	21.1453i	−0.668827	+	0.789687i
$718$		−	56.0751i		−	2.09271i
$719$	−9.21807	−	15.9662i	−0.343776	−	0.595437i	0.641355	−	0.767245i	$-0.278373\pi$
$719$	−9.21807	−	15.9662i	−0.343776	−	0.595437i	−0.985131	+	0.171807i	$0.945039\pi$
$720$	−3.75984	+	10.6873i	−0.140121	+	0.398292i
$721$	−6.30647	+	19.5402i	−0.234865	+	0.727714i
$722$	−36.0793	+	20.8304i	−1.34273	+	0.775228i
$723$	−42.4037	−	7.67775i	−1.57701	−	0.285539i
$724$	−10.7803	−	18.6720i	−0.400645	−	0.693938i
$725$	−1.54300	+	0.0616403i	−0.0573054	+	0.00228926i
$726$	37.4125	+	31.6866i	1.38851	+	1.17600i
$727$	8.41473	−	4.85825i	0.312085	−	0.180182i	−0.335774	−	0.941943i	$-0.608998\pi$
$727$	8.41473	−	4.85825i	0.312085	−	0.180182i	0.647859	+	0.761760i	$0.275665\pi$
$728$	−13.5972	+	12.2916i	−0.503947	+	0.455556i
$729$	12.8510	+	23.7455i	0.475964	+	0.879465i
$730$	4.31971	+	2.38030i	0.159880	+	0.0880988i
$731$	9.58808			0.354628
$732$	−16.6279	−	3.01070i	−0.614584	−	0.111279i
$733$		−	20.1350i		−	0.743703i	−0.928292	−	0.371852i	$-0.878723\pi$
$733$		−	20.1350i		−	0.743703i	0.928292	−	0.371852i	$-0.121277\pi$
$734$	14.7794	−	25.5987i	0.545518	−	0.944865i
$735$	26.2001	+	6.96812i	0.966405	+	0.257023i
$736$	24.5301	+	42.4873i	0.904191	+	1.56610i
$737$	13.9664	−	8.06353i	0.514461	−	0.297024i
$738$	−70.5395	+	11.7714i	−2.59659	+	0.433312i
$739$	5.32968	−	9.23128i	0.196056	−	0.339578i	−0.751190	−	0.660086i	$-0.770520\pi$
$739$	5.32968	−	9.23128i	0.196056	−	0.339578i	0.947246	+	0.320507i	$0.103853\pi$
$740$	13.1551	−	0.262658i	0.483591	−	0.00965551i
$741$	0.181443	−	1.00210i	0.00666547	−	0.0368129i
$742$	0.225581	+	1.05109i	0.00828133	+	0.0385868i
$743$	−31.8796	−	18.4057i	−1.16955	−	0.675240i	−0.215975	−	0.976399i	$-0.569293\pi$
$743$	−31.8796	−	18.4057i	−1.16955	−	0.675240i	−0.953574	+	0.301159i	$0.902626\pi$
$744$	0.150141	−	0.0538677i	0.00550444	−	0.00197489i
$745$	37.5095	−	22.6663i	1.37424	−	0.830429i
$746$	12.7896	−	22.1522i	0.468261	−	0.811051i
$747$	6.33923	−	1.05787i	0.231940	−	0.0387055i
$748$		−	43.0733i		−	1.57492i
$749$	−47.4265	+	10.1785i	−1.73293	+	0.371913i
$750$	−25.4851	+	34.0276i	−0.930584	+	1.24251i
$751$	−41.4084			−1.51101			−0.755507	−	0.655141i	$-0.772609\pi$
$751$	−41.4084			−1.51101			−0.755507	+	0.655141i	$0.772609\pi$
$752$	19.3798	−	11.1889i	0.706710	−	0.408019i
$753$	−19.1313	−	3.46398i	−0.697184	−	0.126235i
$754$	−1.30522	+	2.26071i	−0.0475333	+	0.0823301i
$755$	−9.62246	+	5.81468i	−0.350197	+	0.211618i
$756$	−12.4128	+	36.7226i	−0.451451	+	1.33559i
$757$		−	11.8507i		−	0.430720i	−0.976535	−	0.215360i	$-0.930908\pi$
$757$		−	11.8507i		−	0.430720i	0.976535	−	0.215360i	$-0.0690925\pi$
$758$	−54.7424	−	31.6056i	−1.98833	−	1.14797i
$759$	10.1284	−	55.9386i	0.367639	−	2.03044i
$760$	−0.296556	+	0.538183i	−0.0107572	+	0.0195219i
$761$	48.6006			1.76177			0.880884	−	0.473332i	$-0.156949\pi$
$761$	48.6006			1.76177			0.880884	+	0.473332i	$0.156949\pi$
$762$	1.51777	−	1.79204i	0.0549830	−	0.0649187i
$763$	−23.2793	+	21.0439i	−0.842766	+	0.761840i
$764$	40.2707			1.45694
$765$	−19.7761	−	6.95733i	−0.715006	−	0.251543i
$766$	−4.87283	+	8.43999i	−0.176063	+	0.304949i
$767$			45.2596i			1.63423i
$768$	−2.11949	−	5.90749i	−0.0764807	−	0.213168i
$769$	3.55236	−	6.15287i	0.128101	−	0.221878i	−0.794840	−	0.606820i	$-0.792445\pi$
$769$	3.55236	−	6.15287i	0.128101	−	0.221878i	0.922941	+	0.384941i	$0.125778\pi$
$770$	60.7952	+	18.2896i	2.19091	+	0.659110i
$771$	−5.67313	+	31.3323i	−0.204313	+	1.12840i
$772$	22.7207	+	13.1178i	0.817736	+	0.472120i
$773$	18.3681	+	10.6048i	0.660655	+	0.381429i	0.792526	−	0.609838i	$-0.208765\pi$
$773$	18.3681	+	10.6048i	0.660655	+	0.381429i	−0.131872	+	0.991267i	$0.542099\pi$
$774$	−18.9235	−	7.08499i	−0.680192	−	0.254665i
$775$	−0.255695	+	0.0102146i	−0.00918482	+	0.000366919i
$776$	4.86167	+	8.42066i	0.174524	+	0.302284i
$777$	−9.55838	+	0.308709i	−0.342905	+	0.0110749i
$778$	−32.3852	−	18.6976i	−1.16107	−	0.670341i
$779$	1.65827			0.0594138
$780$	14.9856	+	39.2828i	0.536571	+	1.40655i
$781$	−25.2712			−0.904275
$782$	−39.8956	+	23.0338i	−1.42667	+	0.823686i
$783$	−0.0220967	+	1.60466i	−0.000789671	+	0.0573457i
$784$	10.7811	−	4.85101i	0.385039	−	0.173250i
$785$	−16.6585	+	30.2315i	−0.594568	+	1.07901i
$786$	10.3437	+	8.76057i	0.368946	+	0.312479i
$787$	20.9846	−	12.1154i	0.748019	−	0.431869i	−0.0769587	−	0.997034i	$-0.524521\pi$
$787$	20.9846	−	12.1154i	0.748019	−	0.431869i	0.824978	+	0.565165i	$0.191188\pi$
$788$	−55.4919	+	32.0383i	−1.97682	+	1.14132i
$789$	3.81139	−	21.0500i	0.135689	−	0.749401i
$790$	−25.8141	+	46.8469i	−0.918425	+	1.66674i
$791$	13.2384	+	14.6447i	0.470704	+	0.520705i
$792$	−9.25227	+	24.7122i	−0.328765	+	0.878109i
$793$	11.5367	−	6.66072i	0.409680	−	0.236529i
$794$	−23.2400			−0.824758
$795$	0.707756	+	0.113607i	0.0251015	+	0.00402922i
$796$	−1.80155			−0.0638542
$797$	−27.4779	−	15.8644i	−0.973316	−	0.561944i	−0.0730705	−	0.997327i	$-0.523280\pi$
$797$	−27.4779	−	15.8644i	−0.973316	−	0.561944i	−0.900246	+	0.435382i	$0.856613\pi$
$798$	0.724851	−	1.35467i	0.0256594	−	0.0479548i
$799$	20.7044	+	35.8610i	0.732468	+	1.26867i
$800$	1.45827	+	36.5038i	0.0515576	+	1.29060i
$801$	2.46629	+	14.7791i	0.0871419	+	0.522193i
$802$	5.71690	+	3.30065i	0.201871	+	0.116550i
$803$	−4.25316	−	2.45557i	−0.150091	−	0.0866550i
$804$	12.2954	+	10.4136i	0.433626	+	0.367260i
$805$	−9.10916	−	38.6651i	−0.321056	−	1.36277i
$806$	−0.216292	+	0.374629i	−0.00761856	+	0.0131957i
$807$	15.2648	−	18.0232i	0.537346	−	0.634448i
$808$		−	2.40454i		−	0.0845913i
$809$	−14.0285	+	24.2981i	−0.493216	+	0.854274i	−0.999969	−	0.00781635i	$-0.997512\pi$
$809$	−14.0285	+	24.2981i	−0.493216	+	0.854274i	0.506754	+	0.862091i	$0.330845\pi$
$810$	33.8901	+	28.3446i	1.19078	+	0.995929i
$811$	28.9096			1.01515			0.507576	−	0.861607i	$-0.330542\pi$
$811$	28.9096			1.01515			0.507576	+	0.861607i	$0.330542\pi$
$812$	−1.70918	+	1.54505i	−0.0599803	+	0.0542208i
$813$	−4.45619	−	12.4204i	−0.156285	−	0.435601i
$814$	−22.3949			−0.784942
$815$	8.97579	−	16.2890i	0.314408	−	0.570580i
$816$	−8.60476	+	3.08722i	−0.301227	+	0.108074i
$817$	0.405768	+	0.234270i	0.0141960	+	0.00819609i
$818$		−	43.2477i		−	1.51212i
$819$	−11.2429	−	28.4154i	−0.392859	−	0.992913i
$820$	−58.5944	+	35.4076i	−2.04621	+	1.23649i
$821$	−22.7608	+	39.4229i	−0.794358	+	1.37587i	0.128888	+	0.991659i	$0.458859\pi$
$821$	−22.7608	+	39.4229i	−0.794358	+	1.37587i	−0.923246	+	0.384209i	$0.874474\pi$
$822$	40.8330	−	48.2117i	1.42421	−	1.68158i
$823$	−3.00499	+	1.73493i	−0.104747	+	0.0604759i	−0.551458	−	0.834202i	$-0.685928\pi$
$823$	−3.00499	+	1.73493i	−0.104747	+	0.0604759i	0.446711	+	0.894678i	$0.352595\pi$
$824$	−13.9647			−0.486483
$825$	26.0480	−	33.3695i	0.906874	−	1.16178i
$826$	−20.9722	+	64.9809i	−0.729716	+	2.26097i
$827$		−	0.390724i		−	0.0135868i	−0.999977	−	0.00679341i	$-0.997838\pi$
$827$		−	0.390724i		−	0.0135868i	0.999977	−	0.00679341i	$-0.00216243\pi$
$828$	56.0230	−	9.34895i	1.94693	−	0.324898i
$829$	−12.4790	+	21.6143i	−0.433415	+	0.750697i	−0.997165	−	0.0752487i	$-0.976025\pi$
$829$	−12.4790	+	21.6143i	−0.433415	+	0.750697i	0.563750	+	0.825946i	$0.309358\pi$
$830$	9.00080	−	5.43903i	0.312422	−	0.188791i
$831$	5.29594	−	29.2491i	0.183714	−	1.01464i
$832$	42.2209	+	24.3763i	1.46375	+	0.845095i
$833$	8.97646	+	19.9496i	0.311016	+	0.691214i
$834$	−35.4768	+	12.7284i	−1.22846	+	0.440749i
$835$	17.1012	−	0.341447i	0.591812	−	0.0118163i
$836$	1.05243	−	1.82287i	0.0363991	−	0.0630452i
$837$	−0.00366171	+	0.265912i	−0.000126567	+	0.00919128i
$838$	15.5530	−	8.97952i	0.537269	−	0.310192i
$839$	15.4380	+	26.7394i	0.532979	+	0.923146i	0.999258	+	0.0385089i	$0.0122608\pi$
$839$	15.4380	+	26.7394i	0.532979	+	0.923146i	−0.466279	+	0.884637i	$0.654406\pi$
$840$	0.962974	+	18.4135i	0.0332258	+	0.635326i
$841$	14.4523	−	25.0321i	0.498355	−	0.863177i
$842$			40.4546i			1.39416i
$843$	−3.57000	−	9.95036i	−0.122957	−	0.342709i
$844$	47.8925			1.64853
$845$	−3.56979	−	1.96707i	−0.122804	−	0.0676692i
$846$	−14.3642	−	86.0764i	−0.493850	−	2.95937i
$847$	−32.4644	−	10.4777i	−1.11549	−	0.360018i
$848$	0.270703	−	0.156290i	0.00929596	−	0.00536703i
$849$	−12.1536	+	4.36048i	−0.417110	+	0.149651i
$850$	−34.2771	+	1.36932i	−1.17569	+	0.0469671i
$851$	7.00626	+	12.1352i	0.240171	+	0.415989i
$852$	−8.52660	−	23.7655i	−0.292117	−	0.814192i
$853$	5.55077	−	3.20474i	0.190055	−	0.109728i	−0.401954	−	0.915660i	$-0.631669\pi$
$853$	5.55077	−	3.20474i	0.190055	−	0.109728i	0.592008	+	0.805932i	$0.298335\pi$
$854$	19.6501	−	4.21722i	0.672412	−	0.144310i
$855$	−0.666934	−	0.777634i	−0.0228087	−	0.0265945i
$856$	−16.4951	−	28.5704i	−0.563791	−	0.976515i
$857$		−	9.74505i		−	0.332885i	−0.986051	−	0.166442i	$-0.946772\pi$
$857$		−	9.74505i		−	0.332885i	0.986051	−	0.166442i	$-0.0532279\pi$
$858$	−24.1663	−	67.3566i	−0.825023	−	2.29952i
$859$	21.5922			0.736717			0.368358	−	0.929684i	$-0.379920\pi$
$859$	21.5922			0.736717			0.368358	+	0.929684i	$0.379920\pi$
$860$	−19.3398	+	0.386144i	−0.659482	+	0.0131674i
$861$	42.2676	−	26.2579i	1.44047	−	0.894868i
$862$	−37.2007	+	21.4778i	−1.26706	+	0.731538i
$863$	43.8818	−	25.3351i	1.49375	−	0.862418i	0.493778	−	0.869588i	$-0.335616\pi$
$863$	43.8818	−	25.3351i	1.49375	−	0.862418i	0.999974	+	0.00716968i	$0.00228220\pi$
$864$	37.9625	+	0.522757i	1.29151	+	0.0177846i
$865$	−38.4135	+	0.766973i	−1.30610	+	0.0260779i
$866$	−0.607330	+	1.05193i	−0.0206379	+	0.0357459i
$867$	4.23094	+	11.7925i	0.143690	+	0.400496i
$868$	−0.283233	+	0.256036i	−0.00961355	+	0.00869042i
$869$	26.6304	−	46.1252i	0.903373	−	1.56469i
$870$	0.935973	+	2.45353i	0.0317325	+	0.0831825i
$871$	−12.7022			−0.430398
$872$	−18.4835	−	10.6714i	−0.625929	−	0.361380i
$873$	−15.9896	+	2.66830i	−0.541166	+	0.0903081i
$874$	−2.25118			−0.0761474
$875$	7.38419	−	28.6439i	0.249631	−	0.968341i
$876$	0.874222	−	4.82827i	0.0295372	−	0.163132i
$877$			16.1682i			0.545960i	0.962020	+	0.272980i	$0.0880094\pi$
$877$			16.1682i			0.545960i	−0.962020	+	0.272980i	$0.911991\pi$
$878$	57.2326	−	33.0432i	1.93151	−	1.11515i
$879$	0.763521	+	0.646665i	0.0257529	+	0.0218115i
$880$	−0.368498	−	18.4561i	−0.0124221	−	0.622154i
$881$	−36.4693			−1.22868			−0.614341	−	0.789041i	$-0.710578\pi$
$881$	−36.4693			−1.22868			−0.614341	+	0.789041i	$0.710578\pi$
$882$	−2.97488	−	46.0067i	−0.100169	−	1.54913i
$883$		−	39.3101i		−	1.32289i	−0.749994	−	0.661444i	$-0.769944\pi$
$883$		−	39.3101i		−	1.32289i	0.749994	−	0.661444i	$-0.230056\pi$
$884$	−16.9630	+	29.3807i	−0.570527	+	0.988181i
$885$	35.3233	+	28.7260i	1.18738	+	0.965616i
$886$	16.0165	+	27.7414i	0.538086	+	0.931992i
$887$			45.6381i			1.53238i	0.642615	+	0.766189i	$0.277850\pi$
$887$			45.6381i			1.53238i	−0.642615	+	0.766189i	$0.722150\pi$
$888$	−2.19650	−	6.12213i	−0.0737099	−	0.205445i
$889$	−0.501876	+	1.55503i	−0.0168324	+	0.0521539i
$890$	12.6804	+	20.9842i	0.425046	+	0.703390i
$891$	−33.1758	−	28.8921i	−1.11143	−	0.967921i
$892$	−10.1321	−	5.84976i	−0.339247	−	0.195864i
$893$			2.02352i			0.0677146i
$894$	−56.8708	−	48.1668i	−1.90204	−	1.61094i
$895$	0.826366	+	41.3881i	0.0276224	+	1.38345i
$896$	23.3958	+	25.8810i	0.781600	+	0.864625i
$897$	−28.9383	+	34.1676i	−0.966220	+	1.14082i
$898$	−1.69413	−	0.978107i	−0.0565339	−	0.0326398i
$899$	−0.00790331	+	0.0136889i	−0.000263590	+	0.000456551i
$900$	40.1700	+	13.2370i	1.33900	+	0.441232i
$901$	0.289204	+	0.500916i	0.00963479	+	0.0166879i
$902$	100.913	−	58.2622i	3.36004	−	1.93992i
$903$	14.0521	−	0.453845i	0.467626	−	0.0151030i
$904$	−6.71326	+	11.6277i	−0.223280	+	0.386732i
$905$	14.6338	−	8.84297i	0.486445	−	0.293950i
$906$	14.5893	+	12.3564i	0.484697	+	0.410515i
$907$		−	21.2126i		−	0.704352i	−0.935934	−	0.352176i	$-0.885442\pi$
$907$		−	21.2126i		−	0.704352i	0.935934	−	0.352176i	$-0.114558\pi$
$908$	−32.7772	+	18.9239i	−1.08775	+	0.628012i
$909$	3.75432	+	1.40562i	0.124523	+	0.0466216i
$910$	−34.2663	−	36.4176i	−1.13592	−	1.20723i
$911$	11.8342	+	20.4974i	0.392084	+	0.679109i	0.992724	−	0.120410i	$-0.0384211\pi$
$911$	11.8342	+	20.4974i	0.392084	+	0.679109i	−0.600641	+	0.799519i	$0.705088\pi$
$912$	−0.439586	−	0.0795929i	−0.0145561	−	0.00263558i
$913$	−9.06884	+	5.23590i	−0.300135	+	0.173283i
$914$	−9.51296	−	16.4769i	−0.314661	−	0.545008i
$915$	2.12387	−	13.2315i	0.0702131	−	0.437419i
$916$	−25.1087	−	43.4895i	−0.829614	−	1.43693i
$917$	−8.97562	−	2.89683i	−0.296401	−	0.0956617i
$918$	−0.490869	+	35.6468i	−0.0162011	+	1.17652i
$919$	−14.1751	−	24.5521i	−0.467595	−	0.809898i	0.531720	−	0.846920i	$-0.321546\pi$
$919$	−14.1751	−	24.5521i	−0.467595	−	0.809898i	−0.999314	+	0.0370227i	$0.988213\pi$
$920$	23.1229	−	13.9728i	0.762341	−	0.460669i
$921$	−4.99970	+	27.6130i	−0.164746	+	0.909879i
$922$		−	19.9528i		−	0.657110i
$923$	17.2377	+	9.95222i	0.567387	+	0.327581i
$924$	−2.03884	−	63.1276i	−0.0670730	−	2.07675i
$925$	0.416509	+	10.4262i	0.0136947	+	0.342810i
$926$	−13.3235	−	23.0769i	−0.437836	−	0.758354i
$927$	8.16335	−	21.8038i	0.268120	−	0.716129i
$928$	1.95428	+	1.12830i	0.0641522	+	0.0370383i
$929$	22.5136	−	38.9947i	0.738647	−	1.27937i	−0.214457	−	0.976733i	$-0.568798\pi$
$929$	22.5136	−	38.9947i	0.738647	−	1.27937i	0.953105	−	0.302641i	$-0.0978683\pi$
$930$	0.155103	+	0.406582i	0.00508603	+	0.0133324i
$931$	−0.107555	+	1.06360i	−0.00352498	+	0.0348580i
$932$	−21.5833	−	12.4611i	−0.706984	−	0.408177i
$933$	16.1704	+	45.0704i	0.529395	+	1.47554i
$934$	−12.2600			−0.401160
$935$	34.1517	−	0.681881i	1.11688	−	0.0222999i
$936$	16.0431	−	13.2127i	0.524386	−	0.431872i
$937$			24.9026i			0.813534i	0.913532	+	0.406767i	$0.133344\pi$
$937$			24.9026i			0.813534i	−0.913532	+	0.406767i	$0.866656\pi$
$938$	−18.2370	−	5.88589i	−0.595460	−	0.192181i
$939$	−42.6871	−	36.1539i	−1.39304	−	1.17984i
$940$	−43.2064	−	71.5003i	−1.40924	−	2.33208i
$941$	6.66774	+	11.5489i	0.217362	+	0.376482i	0.954001	−	0.299804i	$-0.0969214\pi$
$941$	6.66774	+	11.5489i	0.217362	+	0.376482i	−0.736639	+	0.676287i	$0.763588\pi$
$942$	57.7585	+	10.4580i	1.88187	+	0.340738i
$943$	−63.1413	−	36.4546i	−2.05616	−	1.18713i
$944$	19.8539			0.646188
$945$	−29.3129	−	9.26047i	−0.953547	−	0.301243i
$946$	32.9236			1.07044
$947$	8.62913	+	4.98203i	0.280409	+	0.161894i	0.633609	−	0.773654i	$-0.281573\pi$
$947$	8.62913	+	4.98203i	0.280409	+	0.161894i	−0.353200	+	0.935548i	$0.614906\pi$
$948$	52.3621	+	9.48085i	1.70064	+	0.307924i
$949$	1.93408	+	3.34993i	0.0627830	+	0.108743i
$950$	−1.48407	−	0.779560i	−0.0481495	−	0.0252923i
$951$	17.7933	+	15.0700i	0.576986	+	0.488679i
$952$	−11.0372	+	9.97734i	−0.357717	+	0.323368i
$953$		−	11.0830i		−	0.359014i	−0.983757	−	0.179507i	$-0.942550\pi$
$953$		−	11.0830i		−	0.359014i	0.983757	−	0.179507i	$-0.0574502\pi$
$954$	−0.200642	−	1.20234i	−0.00649604	−	0.0389271i
$955$	0.637513	+	31.9295i	0.0206294	+	1.03322i
$956$	45.1103			1.45897
$957$	−0.883036	−	2.46121i	−0.0285445	−	0.0795597i
$958$	−23.7112	−	13.6897i	−0.766076	−	0.442294i
$959$	−13.5021	+	41.8353i	−0.436005	+	1.35093i
$960$	45.8221	−	17.4802i	1.47890	−	0.564172i
$961$	15.4987	−	26.8445i	0.499958	−	0.865952i
$962$	15.2758	+	8.81950i	0.492512	+	0.284352i
$963$	54.2509	−	9.05323i	1.74821	−	0.291736i
$964$	35.0762	+	60.7537i	1.12973	+	1.95675i
$965$	−10.0411	+	18.2223i	−0.323234	+	0.586597i
$966$	−57.3802	+	35.6464i	−1.84618	+	1.14690i
$967$	9.04657	+	5.22304i	0.290918	+	0.167962i	0.638356	−	0.769741i	$-0.279615\pi$
$967$	9.04657	+	5.22304i	0.290918	+	0.167962i	−0.347438	+	0.937703i	$0.612948\pi$
$968$		−	23.2012i		−	0.745714i
$969$	0.147281	−	0.813423i	0.00473135	−	0.0261309i
$970$	−22.7029	+	13.7190i	−0.728947	+	0.440490i
$971$	−22.9294	−	39.7149i	−0.735839	−	1.27451i	−0.954354	−	0.298677i	$-0.903455\pi$
$971$	−22.9294	−	39.7149i	−0.735839	−	1.27451i	0.218515	−	0.975834i	$-0.429879\pi$
$972$	15.9770	−	40.9474i	0.512462	−	1.31339i
$973$	19.4545	−	17.5864i	0.623684	−	0.563795i
$974$	−41.9616	−	72.6797i	−1.34454	−	2.32881i
$975$	−30.9091	+	12.5036i	−0.989882	+	0.400434i
$976$	−2.92184	−	5.06077i	−0.0935257	−	0.161991i
$977$	40.4959	−	23.3803i	1.29558	−	0.748004i	0.315943	−	0.948778i	$-0.397679\pi$
$977$	40.4959	−	23.3803i	1.29558	−	0.748004i	0.979637	+	0.200775i	$0.0643459\pi$
$978$	−31.1209	−	5.63486i	−0.995137	−	0.180183i
$979$	−12.2068	−	21.1428i	−0.390130	−	0.675726i
$980$	−18.9096	−	39.8783i	−0.604045	−	1.27387i
$981$	27.4668	−	22.6210i	0.876946	−	0.722232i
$982$	48.0424	−	27.7373i	1.53309	−	0.885132i
$983$		−	43.9289i		−	1.40111i	−0.713597	−	0.700556i	$-0.752935\pi$
$983$		−	43.9289i		−	1.40111i	0.713597	−	0.700556i	$-0.247065\pi$
$984$	25.8248	+	21.8723i	0.823264	+	0.697265i
$985$	−26.2808	−	43.4908i	−0.837374	−	1.38573i
$986$	−1.05948	+	1.83507i	−0.0337406	+	0.0584404i
$987$	32.0415	+	51.5773i	1.01989	+	1.64172i
$988$	−1.43575	+	0.828930i	−0.0456773	+	0.0263718i
$989$	−10.3002	−	17.8404i	−0.327526	−	0.567292i
$990$	−67.9074	−	23.8902i	−2.15824	−	0.759279i
$991$	21.5867	−	37.3892i	0.685724	−	1.18771i	−0.287485	−	0.957785i	$-0.592819\pi$
$991$	21.5867	−	37.3892i	0.685724	−	1.18771i	0.973209	−	0.229923i	$-0.0738474\pi$
$992$	0.323849	+	0.186974i	0.0102822	+	0.00593644i
$993$	6.99492	−	8.25894i	0.221977	−	0.262090i
$994$	20.1373	+	22.2763i	0.638715	+	0.706562i
$995$	−0.0285198	−	1.42840i	−0.000904138	−	0.0452833i
$996$	−7.98379	−	6.76188i	−0.252976	−	0.214258i
$997$		−	11.0208i		−	0.349032i	−0.984654	−	0.174516i	$-0.944164\pi$
$997$		−	11.0208i		−	0.349032i	0.984654	−	0.174516i	$-0.0558361\pi$
$998$	−50.8135	−	29.3372i	−1.60847	−	0.928653i
$999$	10.8428	+	0.149309i	0.343051	+	0.00472394i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bo.b.4.6	yes	84
3.2	odd	2		945.2.bo.b.739.37		84
5.4	even	2	inner	315.2.bo.b.4.37	yes	84
7.2	even	3		315.2.r.b.184.37	yes	84
9.2	odd	6		945.2.r.b.424.6		84
9.7	even	3		315.2.r.b.214.37	yes	84
15.14	odd	2		945.2.bo.b.739.6		84
21.2	odd	6		945.2.r.b.604.6		84
35.9	even	6		315.2.r.b.184.6	✓	84
45.29	odd	6		945.2.r.b.424.37		84
45.34	even	6		315.2.r.b.214.6	yes	84
63.2	odd	6		945.2.bo.b.289.6		84
63.16	even	3	inner	315.2.bo.b.79.37	yes	84
105.44	odd	6		945.2.r.b.604.37		84
315.79	even	6	inner	315.2.bo.b.79.6	yes	84
315.254	odd	6		945.2.bo.b.289.37		84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.r.b.184.6	✓	84	35.9	even	6
315.2.r.b.184.37	yes	84	7.2	even	3
315.2.r.b.214.6	yes	84	45.34	even	6
315.2.r.b.214.37	yes	84	9.7	even	3
315.2.bo.b.4.6	yes	84	1.1	even	1	trivial
315.2.bo.b.4.37	yes	84	5.4	even	2	inner
315.2.bo.b.79.6	yes	84	315.79	even	6	inner
315.2.bo.b.79.37	yes	84	63.16	even	3	inner
945.2.r.b.424.6		84	9.2	odd	6
945.2.r.b.424.37		84	45.29	odd	6
945.2.r.b.604.6		84	21.2	odd	6
945.2.r.b.604.37		84	105.44	odd	6
945.2.bo.b.289.6		84	63.2	odd	6
945.2.bo.b.289.37		84	315.254	odd	6
945.2.bo.b.739.6		84	15.14	odd	2
945.2.bo.b.739.37		84	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bo (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.90125 - 1.09768i) q^{2} +(-1.70434 - 0.308593i) q^{3} +(1.40982 + 2.44189i) q^{4} +(-1.91379 + 1.15647i) q^{5} +(2.90163 + 2.45754i) q^{6} +(-2.51786 - 0.812625i) q^{7} -1.79943i q^{8} +(2.80954 + 1.05190i) q^{9} +O(q^{10})\)	\(q+(-1.90125 - 1.09768i) q^{2} +(-1.70434 - 0.308593i) q^{3} +(1.40982 + 2.44189i) q^{4} +(-1.91379 + 1.15647i) q^{5} +(2.90163 + 2.45754i) q^{6} +(-2.51786 - 0.812625i) q^{7} -1.79943i q^{8} +(2.80954 + 1.05190i) q^{9} +(4.90802 - 0.0979947i) q^{10} -4.88811 q^{11} +(-1.64927 - 4.59686i) q^{12} +(3.33423 + 1.92502i) q^{13} +(3.89507 + 4.30882i) q^{14} +(3.61862 - 1.38043i) q^{15} +(0.844442 - 1.46262i) q^{16} +(2.70647 + 1.56258i) q^{17} +(-4.18698 - 5.08390i) q^{18} +(0.0763587 + 0.132257i) q^{19} +(-5.52207 - 3.04284i) q^{20} +(4.04052 + 2.16199i) q^{21} +(9.29350 + 5.36561i) q^{22} -6.71452i q^{23} +(-0.555292 + 3.06684i) q^{24} +(2.32516 - 4.42647i) q^{25} +(-4.22613 - 7.31987i) q^{26} +(-4.46380 - 2.65979i) q^{27} +(-1.56541 - 7.29400i) q^{28} +(-0.154423 - 0.267468i) q^{29} +(-8.39516 - 1.34757i) q^{30} +(-0.0255899 - 0.0443229i) q^{31} +(-6.32768 + 3.65329i) q^{32} +(8.33100 + 1.50844i) q^{33} +(-3.43044 - 5.94170i) q^{34} +(5.75843 - 1.35664i) q^{35} +(1.39235 + 8.34356i) q^{36} +(-1.80731 + 1.04345i) q^{37} -0.335271i q^{38} +(-5.08861 - 4.30980i) q^{39} +(2.08098 + 3.44372i) q^{40} +(5.42923 - 9.40369i) q^{41} +(-5.30885 - 8.54568i) q^{42} +(2.65699 - 1.53401i) q^{43} +(-6.89138 - 11.9362i) q^{44} +(-6.59335 + 1.23604i) q^{45} +(-7.37042 + 12.7659i) q^{46} +(11.4749 + 6.62506i) q^{47} +(-1.89057 + 2.23220i) q^{48} +(5.67928 + 4.09216i) q^{49} +(-9.27957 + 5.86351i) q^{50} +(-4.13054 - 3.49836i) q^{51} +10.8557i q^{52} +(0.160285 + 0.0925406i) q^{53} +(5.56717 + 9.95676i) q^{54} +(9.35481 - 5.65294i) q^{55} +(-1.46226 + 4.53072i) q^{56} +(-0.0893274 - 0.248975i) q^{57} +0.678030i q^{58} +(5.87781 + 10.1807i) q^{59} +(8.47247 + 6.89009i) q^{60} +(1.73004 - 2.99652i) q^{61} +0.112358i q^{62} +(-6.21924 - 4.93163i) q^{63} +12.6629 q^{64} +(-8.60723 + 0.171854i) q^{65} +(-14.1835 - 12.0127i) q^{66} +(-2.85723 + 1.64962i) q^{67} +8.81185i q^{68} +(-2.07206 + 11.4438i) q^{69} +(-12.4374 - 3.74164i) q^{70} +5.16993 q^{71} +(1.89281 - 5.05557i) q^{72} +(0.870104 + 0.502355i) q^{73} +4.58151 q^{74} +(-5.32884 + 6.82667i) q^{75} +(-0.215305 + 0.372918i) q^{76} +(12.3076 + 3.97220i) q^{77} +(4.94389 + 13.7797i) q^{78} +(-5.44799 + 9.43619i) q^{79} +(0.0753867 + 3.77570i) q^{80} +(6.78703 + 5.91068i) q^{81} +(-20.6446 + 11.9192i) q^{82} +(1.85528 - 1.07115i) q^{83} +(0.417103 + 12.9145i) q^{84} +(-6.98668 + 0.139498i) q^{85} -6.73545 q^{86} +(0.180650 + 0.503510i) q^{87} +8.79581i q^{88} +(2.49724 + 4.32534i) q^{89} +(13.8924 + 4.88740i) q^{90} +(-6.83082 - 7.55642i) q^{91} +(16.3961 - 9.46629i) q^{92} +(0.0299360 + 0.0834381i) q^{93} +(-14.5444 - 25.1917i) q^{94} +(-0.299085 - 0.164806i) q^{95} +(11.9119 - 4.27376i) q^{96} +(-4.67963 + 2.70179i) q^{97} +(-6.30580 - 14.0143i) q^{98} +(-13.7333 - 5.14178i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9}+O(q^{10}) \) 84 * q + 44 * q^4 - 6 * q^5 + 6 * q^6 - 14 * q^9	\( 84 q + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9} + 6 q^{10} - 24 q^{11} - 10 q^{14} + 4 q^{15} - 36 q^{16} + 8 q^{19} - 10 q^{20} - 14 q^{21} + 18 q^{24} + 10 q^{25} - 40 q^{26} - 10 q^{29} - 28 q^{30} - 6 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} + 4 q^{39} - 8 q^{40} - 30 q^{41} - 4 q^{44} - 30 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} + 14 q^{51} + 18 q^{54} - 54 q^{55} + 48 q^{56} + 42 q^{59} + 66 q^{60} + 22 q^{61} - 28 q^{64} + 8 q^{65} - 38 q^{66} - 32 q^{69} - 26 q^{70} - 4 q^{71} - 108 q^{74} + 6 q^{75} + 24 q^{76} + 24 q^{79} - 9 q^{80} - 106 q^{81} - 64 q^{84} + q^{85} - 92 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} - 8 q^{94} - 25 q^{95} + 54 q^{96} - 102 q^{99}+O(q^{100}) \) 84 * q + 44 * q^4 - 6 * q^5 + 6 * q^6 - 14 * q^9 + 6 * q^10 - 24 * q^11 - 10 * q^14 + 4 * q^15 - 36 * q^16 + 8 * q^19 - 10 * q^20 - 14 * q^21 + 18 * q^24 + 10 * q^25 - 40 * q^26 - 10 * q^29 - 28 * q^30 - 6 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 + 4 * q^39 - 8 * q^40 - 30 * q^41 - 4 * q^44 - 30 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 + 14 * q^51 + 18 * q^54 - 54 * q^55 + 48 * q^56 + 42 * q^59 + 66 * q^60 + 22 * q^61 - 28 * q^64 + 8 * q^65 - 38 * q^66 - 32 * q^69 - 26 * q^70 - 4 * q^71 - 108 * q^74 + 6 * q^75 + 24 * q^76 + 24 * q^79 - 9 * q^80 - 106 * q^81 - 64 * q^84 + q^85 - 92 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 - 8 * q^94 - 25 * q^95 + 54 * q^96 - 102 * q^99

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